Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems

Erdös, Pál; Joó, István; Komornik, Vilmos

doi:10.24033/bsmf.2151

Characterization of the unique expansions

1 = \sum_{i = 1}^{\infty} q^{- n_{i}}

and related problems

Erdös, Pál ; Joó, István ; Komornik, Vilmos

Bulletin de la Société Mathématique de France, Tome 118 (1990) no. 3, pp. 377-390

MR Zbl | 6 citations dans Numdam

DOI : 10.24033/bsmf.2151

@article{BSMF_1990__118_3_377_0,
     author = {Erd\"os, P\'al and Jo\'o, Istv\'an and Komornik, Vilmos},
     title = {Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {377--390},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {118},
     number = {3},
     year = {1990},
     doi = {10.24033/bsmf.2151},
     mrnumber = {91j:11006},
     zbl = {0721.11005},
     language = {en},
     url = {https://numdam.org/articles/10.24033/bsmf.2151/}
}

TY  - JOUR
AU  - Erdös, Pál
AU  - Joó, István
AU  - Komornik, Vilmos
TI  - Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems
JO  - Bulletin de la Société Mathématique de France
PY  - 1990
SP  - 377
EP  - 390
VL  - 118
IS  - 3
PB  - Société mathématique de France
UR  - https://numdam.org/articles/10.24033/bsmf.2151/
DO  - 10.24033/bsmf.2151
LA  - en
ID  - BSMF_1990__118_3_377_0
ER  -

%0 Journal Article
%A Erdös, Pál
%A Joó, István
%A Komornik, Vilmos
%T Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems
%J Bulletin de la Société Mathématique de France
%D 1990
%P 377-390
%V 118
%N 3
%I Société mathématique de France
%U https://numdam.org/articles/10.24033/bsmf.2151/
%R 10.24033/bsmf.2151
%G en
%F BSMF_1990__118_3_377_0

Erdös, Pál; Joó, István; Komornik, Vilmos. Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems. Bulletin de la Société Mathématique de France, Tome 118 (1990) no. 3, pp. 377-390. doi: 10.24033/bsmf.2151

Bibliographie
Cité par

[1] Rényi (A.). - Representations for real numbers and their ergodic properties, Acta Math. Hungar., t. 8, 1957, p. 477-493. | Zbl | MR

[2] Parry (W.). - On the β-expansions of real numbers, Acta Math. Hungar., t. 11, 1960, p. 401-416. | Zbl | MR

[3] Bertrand (A.). - Développements en base de Pisot et répartition modulo 1 de la suite ({x΋n}), Thèse de 3ème cycle, Université de Bordeaux I, n° 1595, 1981.

[4] Erdös (P.) and Joó (I.). - On the expansions 1 = Σq-ni, 1 < q < 2, to appear.

[5] Erdös (P.), Horváth (M.) and Joó (I.). - On the uniqueness of the expansions 1 = Σq-ni, to appear.

[6] Joó (I.). - On the distribution of the set {ΣNi=1 εiqi : εi = 0,1}, to appear. | Zbl

[7] Joó (I.) and Joó (M.). - On an arithmetical property of √2, to appear.

[8] Bogmér (A.), Horváth (M.) and Sövegjártó (A.). - On some problems of I. JOÓ, to appear.

[9] Rauzy (G.). - Sur les développements en base non entière, [Colloque de Théorie des nombres, Alger], 21-23 octobre 1989, to appear.

Riabov, Volodymyr Mesoscopic eigenvalue statistics for Wigner-type matrices, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 61 (2025) no. 1 | DOI:10.1214/23-aihp1438
Anashin, Vladimir Applications to Foundations of Quantum Theory, Causality: The p-adic Theory (2025), p. 341 | DOI:10.1007/978-3-031-85818-5_16
Kong, Derong; Sun, Beibei Projections of four corner Cantor set: total self-similarity, spectrum and unique codings, Indagationes Mathematicae. New Series, Volume 36 (2025) no. 3, pp. 764-796 | DOI:10.1016/j.indag.2024.08.006 | Zbl:8031093
Yi, Cai; Wenxia, Li Bases which admit exactly n expansions, SCIENTIA SINICA Mathematica (2025) | DOI:10.1360/ssm-2025-0029
Hu, Yuecai; Alcaraz Barrera, Rafael; Zou, Yuru Topological and dimensional properties of univoque bases in double-base expansions, Topology and its Applications, Volume 366 (2025), p. 31 (Id/No 109294) | DOI:10.1016/j.topol.2025.109294 | Zbl:8009166
Cai, Yi; Komornik, Vilmos Hausdorff distance of univoque sets, Topology and its Applications, Volume 368 (2025), p. 11 (Id/No 109378) | DOI:10.1016/j.topol.2025.109378 | Zbl:8037421
Huang, Yan; Kalle, Charlene Rational approximation with generalised $α$ -Lüroth expansions, Acta Arithmetica, Volume 215 (2024) no. 4, pp. 327-353 | DOI:10.4064/aa230717-4-3 | Zbl:7927172
Lai, A. C.; Loreti, P. Optimal expansions of Kakeya sequences, Acta Mathematica Hungarica, Volume 174 (2024) no. 1, pp. 1-19 | DOI:10.1007/s10474-024-01453-8 | Zbl:7966614
McKenna, Benjamin Complexity of bipartite spherical spin glasses, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 60 (2024) no. 1 | DOI:10.1214/22-aihp1327
Kalle, Charlene; Verbitskiy, Evgeny; Zeegers, Benthen Pseudo-random number generation with $β$ -encoders, International Journal of Mathematics for Industry, Volume 16 (2024) no. 1, p. 11 (Id/No 2450026) | DOI:10.1142/s2661335224500266 | Zbl:8005739
Komornik, Vilmos; Loreti, Paola; Pedicini, Marco A quasi-ergodic approach to non-integer base expansions, Journal of Number Theory, Volume 254 (2024), pp. 146-168 | DOI:10.1016/j.jnt.2023.07.009 | Zbl:1530.11010
Charlier, Émilie; Cisternino, Célia; Kreczman, Savinien On periodic alternate base expansions, Journal of Number Theory, Volume 254 (2024), pp. 184-198 | DOI:10.1016/j.jnt.2023.07.008 | Zbl:1536.11120
Li, Rao; Lü, Fan Run-length function of the beta-expansion of a fixed real number, Journal of Number Theory, Volume 256 (2024), pp. 55-78 | DOI:10.1016/j.jnt.2023.09.002 | Zbl:1540.11100
Komornik, Vilmos; Steiner, Wolfgang; Zou, Yuru Unique double base expansions, Monatshefte für Mathematik, Volume 204 (2024) no. 3, pp. 513-542 | DOI:10.1007/s00605-024-01973-z | Zbl:1545.11007
Hbaib, M.; Guidara, S.; Zouari, S. On the conjecture of Erdős, Joò and Komornik for $p$ -adic numbers, Research in Number Theory, Volume 10 (2024) no. 3, p. 8 (Id/No 71) | DOI:10.1007/s40993-024-00558-x | Zbl:7899210
Li, Yao-Qiang Expansions of generalized Thue-Morse numbers, Advances in Applied Mathematics, Volume 143 (2023), p. 18 (Id/No 102456) | DOI:10.1016/j.aam.2022.102456 | Zbl:1532.11037
Anashin, Vladimir Free Choice in Quantum Theory: A p-adic View, Entropy, Volume 25 (2023) no. 5, p. 830 | DOI:10.3390/e25050830
Tierce, Younès The natural extension of the random beta-transformation, Ergodic Theory and Dynamical Systems, Volume 43 (2023) no. 11, pp. 3861-3896 | DOI:10.1017/etds.2022.79 | Zbl:1533.37116
Charlier, Émilie; Cisternino, Célia; Dajani, Karma Dynamical behavior of alternate base expansions, Ergodic Theory and Dynamical Systems, Volume 43 (2023) no. 3, pp. 827-860 | DOI:10.1017/etds.2021.161 | Zbl:1525.11009
Mackenzie, Andrew; Komornik, Vilmos Fairly taking turns, Games and Economic Behavior, Volume 142 (2023), pp. 743-764 | DOI:10.1016/j.geb.2023.09.005 | Zbl:1530.91247
Baker, Simon; Zou, Yuru Metric results for numbers with multiple $q$ -expansions, Journal of Fractal Geometry, Volume 10 (2023) no. 3-4, pp. 243-266 | DOI:10.4171/jfg/131 | Zbl:1542.11068
Hu, Yu; Huang, Yan; Kong, Derong Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals, Journal of Number Theory, Volume 247 (2023), pp. 46-74 | DOI:10.1016/j.jnt.2022.12.005 | Zbl:1520.11010
Li, Yao-Qiang Bifurcations of digit frequencies in unique expansions, Journal of Number Theory, Volume 248 (2023), pp. 420-446 | DOI:10.1016/j.jnt.2022.12.008 | Zbl:1523.11010
Charlier, Émilie; Cisternino, Célia; Masáková, Zuzana; Pelantová, Edita Spectrum, algebraicity and normalization in alternate bases, Journal of Number Theory, Volume 249 (2023), pp. 470-499 | DOI:10.1016/j.jnt.2023.02.012 | Zbl:1523.11135
Landon, Benjamin; Noack, Christian; Sosoe, Philippe KPZ-type fluctuation exponents for interacting diffusions in equilibrium, The Annals of Probability, Volume 51 (2023) no. 3 | DOI:10.1214/22-aop1617
Komornik, V.; Lu, J.; Zou, Y. Expansions in multiple bases over general alphabets, Acta Mathematica Hungarica, Volume 166 (2022) no. 2, pp. 481-506 | DOI:10.1007/s10474-022-01231-4 | Zbl:1524.11015
Vargas, Victor On involution kernels and large deviations principles on $β$ -shifts, Discrete and Continuous Dynamical Systems, Volume 42 (2022) no. 6, pp. 2699-2718 | DOI:10.3934/dcds.2021208 | Zbl:1506.11106
Kalle, Charlene; Maggioni, Marta Invariant densities for random systems of the interval, Ergodic Theory and Dynamical Systems, Volume 42 (2022) no. 1, pp. 141-179 | DOI:10.1017/etds.2020.127 | Zbl:1486.37022
Zou, Yuru; Lu, Jian; Komornik, Vilmos Hausdorff dimension of multiple expansions, Journal of Number Theory, Volume 233 (2022), pp. 198-227 | DOI:10.1016/j.jnt.2021.06.009 | Zbl:1484.11023
de Vries, Martijn; Komornik, Vilmos; Loreti, Paola Topology of univoque sets in real base expansions, Topology and its Applications, Volume 312 (2022), p. 36 (Id/No 108085) | DOI:10.1016/j.topol.2022.108085 | Zbl:1504.11015
Li, Y.-Q. Expansions in multiple bases, Acta Mathematica Hungarica, Volume 163 (2021) no. 2, pp. 576-600 | DOI:10.1007/s10474-020-01094-7 | Zbl:1474.11026
Dajani, Karma; Jiang, Kan; Kong, Derong; Li, Wenxia; Xi, Lifeng Multiple codings of self-similar sets with overlaps, Advances in Applied Mathematics, Volume 124 (2021), p. 50 (Id/No 102146) | DOI:10.1016/j.aam.2020.102146 | Zbl:1484.11014
Baiocchi, Claudio; Komornik, Vilmos; Loreti, Paola Fibonacci expansions, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni, Volume 32 (2021) no. 3, pp. 379-389 | DOI:10.4171/rlm/940 | Zbl:1484.11011
Li, Yao-Qiang Hausdorff dimension of frequency sets of univoque sequences, Dynamical Systems, Volume 36 (2021) no. 2, pp. 340-361 | DOI:10.1080/14689367.2021.1905778 | Zbl:1472.37016
Allaart, Pieter; Kong, Derong Relative bifurcation sets and the local dimension of univoque bases, Ergodic Theory and Dynamical Systems, Volume 41 (2021) no. 8, pp. 2241-2273 | DOI:10.1017/etds.2020.38 | Zbl:1475.11014
Alcaraz Barrera, Rafael On the specification property and synchronization of unique $q$ -expansions, Ergodic Theory and Dynamical Systems, Volume 41 (2021) no. 9, pp. 2659-2705 | DOI:10.1017/etds.2020.55 | Zbl:1477.37019
Vávra, Tomáš Periodic representations in Salem bases, Israel Journal of Mathematics, Volume 242 (2021) no. 1, pp. 83-95 | DOI:10.1007/s11856-021-2123-3 | Zbl:1478.11131
Ambrož, Petr; Masáková, Zuzana; Pelantová, Edita Lattice bounded distance equivalence for 1D Delone sets with finite local complexity, Journal of Geometry and Symmetry in Physics, Volume 59 (2021), pp. 1-29 | DOI:10.7546/jgsp-59-2021-1-29 | Zbl:1515.11074
Neunhäuserer, Jörg Non-uniform expansions of real numbers, Mediterranean Journal of Mathematics, Volume 18 (2021) no. 2, p. 8 (Id/No 70) | DOI:10.1007/s00009-021-01723-7 | Zbl:1468.11163
Jitsumatsu, Yutaka Invariant set of two-dimensional dynamics of golden ratio encoders, Nonlinear Theory and Its Applications, IEICE, Volume 12 (2021) no. 1, p. 75 | DOI:10.1587/nolta.12.75
Zou, Yuru; Li, Jiachang; Lu, Jian; Komornik, Vilmos Univoque graphs for non-integer base expansions, Science China. Mathematics, Volume 64 (2021) no. 12, pp. 2667-2702 | DOI:10.1007/s11425-020-1763-5 | Zbl:1484.11022
Allaart, Pieter; Kong, Derong On the smallest base in which a number has a unique expansion, Transactions of the American Mathematical Society, Volume 374 (2021) no. 9, pp. 6201-6249 | DOI:10.1090/tran/8332 | Zbl:1491.11010
Li, Y.-Q. Digit frequencies of beta-expansions, Acta Mathematica Hungarica, Volume 162 (2020) no. 2, pp. 403-418 | DOI:10.1007/s10474-020-01032-7 | Zbl:1474.11025
Kong, Derong; Li, Wenxia; Lü, Fan; Wang, Zhiqiang; Xu, Jiayi Univoque bases of real numbers: local dimension, devil's staircase and isolated points, Advances in Applied Mathematics, Volume 121 (2020), p. 31 (Id/No 102103) | DOI:10.1016/j.aam.2020.102103 | Zbl:1459.11022
Hamidoğlu, Ali; Mahmudov, Elimhan N. On topology of polynomial type sequences with bounded integer coefficients, Filomat, Volume 34 (2020) no. 13, pp. 4575-4587 | DOI:10.2298/fil2013575h | Zbl:1499.11032
Zhao, Bing; Ren, Xiaomin; Zhu, Jiali; Jiang, Kan Arithmetic on self-similar sets, Indagationes Mathematicae. New Series, Volume 31 (2020) no. 4, pp. 595-606 | DOI:10.1016/j.indag.2020.05.003 | Zbl:1446.28011
Quackenbush, Blaine; Samuel, Tony; West, Matt Periodic Intermediate β-Expansions of Pisot Numbers, Mathematics, Volume 8 (2020) no. 6, p. 903 | DOI:10.3390/math8060903
Lopes, Artur O.; Vargas, Victor The Ruelle operator for symmetric $β$ -shifts, Publicacions Matemàtiques, Volume 64 (2020) no. 2, pp. 661-680 | DOI:10.5565/publmat6422012 | Zbl:1459.37029
Dajani, Karma; Kong, Derong; Yao, Yuanyuan On the structure of $λ$ -Cantor set with overlaps, Advances in Applied Mathematics, Volume 108 (2019), pp. 97-125 | DOI:10.1016/j.aam.2019.04.003 | Zbl:1416.28009
Allaart, Pieter; Kong, Derong On the continuity of the Hausdorff dimension of the univoque set, Advances in Mathematics, Volume 354 (2019), p. 24 (Id/No 106729) | DOI:10.1016/j.aim.2019.106729 | Zbl:1473.11015
Kwon, Doyong Sturmian words and Cantor sets arising from unique expansions over ternary alphabets, Ergodic Theory and Dynamical Systems, Volume 39 (2019) no. 10, pp. 2827-2854 | DOI:10.1017/etds.2017.136 | Zbl:1443.11150
Suzuki, Shintaro Invariant density functions of random $β$ -transformations, Ergodic Theory and Dynamical Systems, Volume 39 (2019) no. 4, pp. 1099-1120 | DOI:10.1017/etds.2017.64 | Zbl:1432.37008
Komornik, Vilmos; Kong, Derong Bases in which some numbers have exactly two expansions, Journal of Number Theory, Volume 195 (2019), pp. 226-268 | DOI:10.1016/j.jnt.2018.06.004 | Zbl:1447.11006
Tan, Bo; Zhang, Liling On small bases which admit countably many expansions with multiple digits, Journal of Number Theory, Volume 196 (2019), pp. 87-113 | DOI:10.1016/j.jnt.2018.09.021 | Zbl:1454.11020
Baker, Simon; Kong, Derong Numbers with simply normal $β$ -expansions, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 167 (2019) no. 1, pp. 171-192 | DOI:10.1017/s0305004118000270 | Zbl:1435.11017
Dajani, Karma; Jiang, Kan; Kong, Derong; Li, Wenxia Multiple expansions of real numbers with digits set ${0, 1, q}$ , Mathematische Zeitschrift, Volume 291 (2019) no. 3-4, pp. 1605-1619 | DOI:10.1007/s00209-018-2123-0 | Zbl:1473.11016
Šíma, Jiří Subrecursive neural networks, Neural Networks, Volume 116 (2019), pp. 208-223 | DOI:10.1016/j.neunet.2019.04.019 | Zbl:1434.68168
Li, Bing; Sahlsten, Tuomas; Samuel, Tony; Steiner, Wolfgang Denseness of intermediate $β$ -shifts of finite-type, Proceedings of the American Mathematical Society, Volume 147 (2019) no. 5, pp. 2045-2055 | DOI:10.1090/proc/14279 | Zbl:1442.37027
Alcaraz Barrera, Rafael; Baker, Simon; Kong, Derong Entropy, topological transitivity, and dimensional properties of unique $q$ -expansions, Transactions of the American Mathematical Society, Volume 371 (2019) no. 5, pp. 3209-3258 | DOI:10.1090/tran/7370 | Zbl:1435.11016
Bandt, Christoph Finite orbits in multivalued maps and Bernoulli convolutions, Advances in Mathematics, Volume 324 (2018), pp. 437-485 | DOI:10.1016/j.aim.2017.11.011 | Zbl:1382.37007
Dajani, K.; Komornik, V.; Loreti, P. Notes on some of Kahane's works: Ingham type theorems and Bernoulli convolutions, Analysis Mathematica, Volume 44 (2018) no. 2, pp. 207-217 | DOI:10.1007/s10476-018-0206-0 | Zbl:1399.11029
Hare, Kevin G.; Masáková, Zuzana; Vávra, Tomáš On the spectra of Pisot-cyclotomic numbers, Letters in Mathematical Physics, Volume 108 (2018) no. 7, pp. 1729-1756 | DOI:10.1007/s11005-018-1053-4 | Zbl:1395.52026
Šíma, Jiří; Savický, Petr Quasi-periodic $β$ -expansions and cut languages, Theoretical Computer Science, Volume 720 (2018), pp. 1-23 | DOI:10.1016/j.tcs.2018.02.028 | Zbl:1388.68180
Sima, Jiri, 2017 International Joint Conference on Neural Networks (IJCNN) (2017), p. 154 | DOI:10.1109/ijcnn.2017.7965849
Komornik, V.; Pedicini, M. Critical bases for ternary alphabets, Acta Mathematica Hungarica, Volume 152 (2017) no. 1, pp. 25-57 | DOI:10.1007/s10474-017-0706-6 | Zbl:1399.11031
Baiocchi, C.; Komornik, V.; Loreti, P. Cantor type functions in non-integer bases, Acta Mathematica Hungarica, Volume 153 (2017) no. 1, pp. 83-108 | DOI:10.1007/s10474-017-0732-4 | Zbl:1399.11026
GE, Yuehua; TAN, Bo Periodicity of the univoque β-expansions, Acta Mathematica Scientia, Volume 37 (2017) no. 1, p. 33 | DOI:10.1016/s0252-9602(16)30113-8
Komornik, Vilmos; Pedicini, Marco; Pethő, Attila Multiple common expansions in non-integer bases, Acta Scientiarum Mathematicarum, Volume 83 (2017) no. 1-2, p. 51 | DOI:10.14232/actasm-015-080-0
Komornik, Vilmos; Kong, Derong; Li, Wenxia Hausdorff dimension of univoque sets and devil's staircase, Advances in Mathematics, Volume 305 (2017), pp. 165-196 | DOI:10.1016/j.aim.2016.03.047 | Zbl:1362.11075
Allaart, Pieter C. On univoque and strongly univoque sets, Advances in Mathematics, Volume 308 (2017), pp. 575-598 | DOI:10.1016/j.aim.2016.12.029 | Zbl:1362.11074
Kallós, Gábor Supplement to paper “On some problems of expansions investigated by P. Erdős et al.”, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica, Volume 46 (2017), pp. 97-103 | Zbl:1399.11030
Baker, Simon; Steiner, Wolfgang On the regularity of the generalised golden ratio function, Bulletin of the London Mathematical Society, Volume 49 (2017) no. 1, pp. 58-70 | DOI:10.1112/blms.12002 | Zbl:1396.11011
Cao, Chunyun; Chen, Yuanhong The run-length function of the $β$ -expansion of the unit, Journal of Number Theory, Volume 177 (2017), pp. 248-262 | DOI:10.1016/j.jnt.2017.01.015 | Zbl:1426.11078
Kong, Derong; Li, Wenxia; Lü, Fan; de Vries, Martijn Univoque bases and Hausdorff dimension, Monatshefte für Mathematik, Volume 184 (2017) no. 3, pp. 443-458 | DOI:10.1007/s00605-017-1047-9 | Zbl:1417.11006
Jiang, Kan; Dajani, Karma Subshifts of finite type and self-similar sets, Nonlinearity, Volume 30 (2017) no. 2, pp. 659-686 | DOI:10.1088/1361-6544/aa53c7 | Zbl:1364.37029
Baker, Simon; Kong, Derong Unique expansions and intersections of Cantor sets, Nonlinearity, Volume 30 (2017) no. 4, p. 1497 | DOI:10.1088/1361-6544/aa6078
Bandt, Christoph The two-dimensional density of Bernoulli convolutions, Recent developments in fractals and related fields. Conference on fractals and related fields III, Ile de Porquerolles, France, September 2015, Cham: Birkhäuser/Springer, 2017, pp. 39-55 | DOI:10.1007/978-3-319-57805-7_2 | Zbl:1390.28011
Allouche, Jean-Paul Some Extremalities of the Binary Fibonacci Sequence, The Fibonacci Quarterly, Volume 55 (2017) no. 5, p. 1 | DOI:10.1080/00150517.2017.12427729
Kong, D. On small univoque bases of real numbers, Acta Mathematica Hungarica, Volume 150 (2016) no. 1, pp. 194-208 | DOI:10.1007/s10474-016-0637-7 | Zbl:1399.11032
de Vries, Martijn; Komornik, Vilmos Expansions in non-integer bases, Combinatorics, words and symbolic dynamics, Cambridge: Cambridge University Press, 2016, p. 18 | DOI:10.1017/cbo9781139924733.003 | Zbl:1407.11015
Zou, Yuru; Li, Wenxia; Lu, Jian On the cardinality of β-expansions of some numbers, International Journal of Number Theory, Volume 12 (2016) no. 06, p. 1497 | DOI:10.1142/s1793042116500925
Zou, Yuru; Kong, Derong On a problem of countable expansions, Journal of Number Theory, Volume 158 (2016), pp. 134-150 | DOI:10.1016/j.jnt.2015.06.017 | Zbl:1362.11008
Hu, Hui; Tong, Xin; Yu, Yueli On consecutive 0 digits in the $β$ -expansion of 1, Journal of Number Theory, Volume 166 (2016), pp. 219-234 | DOI:10.1016/j.jnt.2016.02.019 | Zbl:1414.11097
Feng, De-Jun On the topology of polynomials with bounded integer coefficients, Journal of the European Mathematical Society (JEMS), Volume 18 (2016) no. 1, pp. 181-193 | DOI:10.4171/jems/587 | Zbl:1332.11066
Komornik, Vilmos Locally Convex Spaces, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 119 | DOI:10.1007/978-1-4471-6811-9_3
Komornik, Vilmos Monotone Functions, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 151 | DOI:10.1007/978-1-4471-6811-9_4
Komornik, Vilmos The Lebesgue Integral in $R$ , Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 169 | DOI:10.1007/978-1-4471-6811-9_5
Komornik, Vilmos Generalized Newton–Leibniz Formula, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 197 | DOI:10.1007/978-1-4471-6811-9_6
Komornik, Vilmos Integrals on Measure Spaces, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 211 | DOI:10.1007/978-1-4471-6811-9_7
Komornik, Vilmos Spaces of Continuous Functions, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 257 | DOI:10.1007/978-1-4471-6811-9_8
Komornik, Vilmos Hilbert Spaces, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 3 | DOI:10.1007/978-1-4471-6811-9_1
Komornik, Vilmos Spaces of Integrable Functions, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 305 | DOI:10.1007/978-1-4471-6811-9_9
Komornik, Vilmos Almost Everywhere Convergence, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 341 | DOI:10.1007/978-1-4471-6811-9_10
Komornik, Vilmos Banach Spaces, Lectures on Functional Analysis and the Lebesgue Integral (2016), p. 55 | DOI:10.1007/978-1-4471-6811-9_2
Hejda, Tomáš; Pelantová, Edita Spectral properties of cubic complex Pisot units, Mathematics of Computation, Volume 85 (2016) no. 297, pp. 401-421 | DOI:10.1090/mcom/2983 | Zbl:1400.11022
Zou, Yuru; Wang, Lijin; Lu, Jian; Baker, Simon On small bases for which 1 has countably many expansions, Mathematika, Volume 62 (2016) no. 2, pp. 362-377 | DOI:10.1112/s002557931500025x | Zbl:1419.11015
Baker, Simon On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure, Monatshefte für Mathematik, Volume 179 (2016) no. 1, pp. 1-13 | DOI:10.1007/s00605-015-0755-2 | Zbl:1345.28012
Jitsumatsu, Yutaka; Matsumura, Kazuya A β-ary to binary conversion for random number generation using a β encoder, Nonlinear Theory and Its Applications, IEICE, Volume 7 (2016) no. 1, p. 38 | DOI:10.1587/nolta.7.38
de Vries, Martijn; Komornik, Vilmos; Loreti, Paola Topology of the set of univoque bases, Topology and its Applications, Volume 205 (2016), pp. 117-137 | DOI:10.1016/j.topol.2016.01.023 | Zbl:1362.11010
Boyland, Philip; De Carvalho, André; Hall, Toby On digit frequencies in $β$ -expansions, Transactions of the American Mathematical Society, Volume 368 (2016) no. 12, pp. 8633-8674 | DOI:10.1090/tran/6617 | Zbl:1419.11011
Dombek, Daniel; Masáková, Zuzana; Vávra, Tomáš Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems, Journal de Théorie des Nombres de Bordeaux, Volume 27 (2015) no. 3, pp. 745-768 | DOI:10.5802/jtnb.922 | Zbl:1397.11014
Baker, Simon On small bases which admit countably many expansions, Journal of Number Theory, Volume 147 (2015), pp. 515-532 | DOI:10.1016/j.jnt.2014.08.003 | Zbl:1386.11022
Masáková, Zuzana; Pastirčáková, Kateřina; Pelantová, Edita Description of spectra of quadratic Pisot units, Journal of Number Theory, Volume 150 (2015), pp. 168-190 | DOI:10.1016/j.jnt.2014.11.011 | Zbl:1316.11067
Kong, Derong; Li, Wenxia Hausdorff dimension of unique beta expansions, Nonlinearity, Volume 28 (2015) no. 1, p. 187 | DOI:10.1088/0951-7715/28/1/187
Baker, S. On universal and periodic $β$ -expansions, and the Hausdorff dimension of the set of all expansions, Acta Mathematica Hungarica, Volume 142 (2014) no. 1, pp. 95-109 | DOI:10.1007/s10474-013-0366-0 | Zbl:1299.11052
Vince, A. A combinatorial approach to binary positional number systems, Acta Mathematica Hungarica, Volume 143 (2014) no. 1, pp. 138-158 | DOI:10.1007/s10474-013-0387-8 | Zbl:1324.11051
Alcaraz Barrera, Rafael Topological and ergodic properties of symmetric sub-shifts, Discrete and Continuous Dynamical Systems, Volume 34 (2014) no. 11, pp. 4459-4486 | DOI:10.3934/dcds.2014.34.4459 | Zbl:1351.37051
Ben Amar, Héla; Gadri, Wiem; Mkaouar, Mohamed A proof of the Erdős-Joó-Komornik conjecture in the case of formal power series, Monatshefte für Mathematik, Volume 175 (2014) no. 2, pp. 161-173 | DOI:10.1007/s00605-013-0595-x | Zbl:1303.11117
Masáková, Z.; Pelantová, E. Optimal number representations in negative base, Acta Mathematica Hungarica, Volume 140 (2013) no. 4, pp. 329-340 | DOI:10.1007/s10474-013-0336-6 | Zbl:1299.11053
Bonanno, Claudio; Carminati, Carlo; Isola, Stefano; Tiozzo, Giulio Dynamics of continued fractions and kneading sequences of unimodal maps, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 4, p. 1313 | DOI:10.3934/dcds.2013.33.1313
Akiyama, Shigeki; Komornik, Vilmos Discrete spectra and Pisot numbers, Journal of Number Theory, Volume 133 (2013) no. 2, pp. 375-390 | DOI:10.1016/j.jnt.2012.07.015 | Zbl:1285.11106
Hejda, Tomáš; Masáková, Zuzana; Pelantová, Edita Greedy and lazy representations in negative base systems, Kybernetika, Volume 49 (2013) no. 2, pp. 258-279 | Zbl:1275.11020
Komornik, Vilmos Unique infinite expansions in noninteger bases, Acta Mathematica Hungarica, Volume 134 (2012) no. 3, p. 344 | DOI:10.1007/s10474-011-0148-5
Kohda, Tohru; Horio, Yoshihiko; Aihara, Kazuyuki $β$ -expansion attractors observed in A/D converters, Chaos, Volume 22 (2012) no. 4, p. 047512 | DOI:10.1063/1.4758813 | Zbl:1319.37023
Epifanio, C.; Frougny, C.; Gabriele, A.; Mignosi, F.; Shallit, J. Sturmian graphs and integer representations over numeration systems, Discrete Applied Mathematics, Volume 160 (2012) no. 4-5, pp. 536-547 | DOI:10.1016/j.dam.2011.10.029 | Zbl:1237.68134
KOHDA, TOHRU; HORIO, YOSHIHIKO; TAKAHASHI, YOICHIRO; AIHARA, KAZUYUKI BETA ENCODERS: SYMBOLIC DYNAMICS AND ELECTRONIC IMPLEMENTATION, International Journal of Bifurcation and Chaos, Volume 22 (2012) no. 09, p. 1230031 | DOI:10.1142/s0218127412300315
Zou, Yuru; Lu, Jian; Li, Wenxia Unique expansion of points of a class of self-similar sets with overlaps, Mathematika, Volume 58 (2012) no. 2, pp. 371-388 | DOI:10.1112/s0025579312000083 | Zbl:1251.28006
Kohda, Tohru; Horio, Yoshihiko; Aihara, Kazuyuki β-Expansion's Attractors Observed in A/D Converters, Procedia IUTAM, Volume 5 (2012), p. 187 | DOI:10.1016/j.piutam.2012.06.024
Kalle, Charlene; Steiner, Wolfgang Beta-expansions, natural extensions and multiple tilings associated with Pisot units, Transactions of the American Mathematical Society, Volume 364 (2012) no. 5, pp. 2281-2318 | DOI:10.1090/s0002-9947-2012-05362-1 | Zbl:1295.11010
Lai, Anna Chiara Minimal unique expansions with digits in ternary alphabets, Indagationes Mathematicae. New Series, Volume 21 (2011) no. 1-2, pp. 1-15 | DOI:10.1016/j.indag.2010.11.001 | Zbl:1235.11015
JORDAN, THOMAS; SHMERKIN, PABLO; SOLOMYAK, BORIS Multifractal structure of Bernoulli convolutions, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 151 (2011) no. 3, p. 521 | DOI:10.1017/s0305004111000466
Feng, De-Jun; Sidorov, Nikita Growth rate for beta-expansions, Monatshefte für Mathematik, Volume 162 (2011) no. 1, p. 41 | DOI:10.1007/s00605-010-0192-1
Zaïmi, Toufik A property of the spectra of non-Pisot numbers, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 348 (2010) no. 3-4, pp. 121-124 | DOI:10.1016/j.crma.2010.01.016 | Zbl:1225.11133
Komornik, Vilmos; Loreti, Paola Universal Expansions in Negative and Complex Bases, Integers, Volume 10 (2010) no. 6 | DOI:10.1515/integ.2010.050
Zaïmi, Toufik Comments on some results about Pisot numbers, Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 513-524 | DOI:10.5802/jtnb.729 | Zbl:1223.11130
Kong, Derong; Li, Wenxia; Dekking, F Michel Intersections of homogeneous Cantor sets and beta-expansions, Nonlinearity, Volume 23 (2010) no. 11, p. 2815 | DOI:10.1088/0951-7715/23/11/005
Allouche, Jean-Paul; Wen, Zhi-Xiong Univoque numbers and automatic sequences, Recent developments in fractals and related fields. Based on the international conference on fractals and related fields, Monastir, Tunisia, September 2007 held in honor of Jacques Peyrière, Boston, MA: Birkhäuser, 2010, pp. 383-392 | DOI:10.1007/978-0-8176-4888-6_24 | Zbl:1220.68075
Dajani, K.; Kalle, C. A natural extension for the greedy β-transformation with three arbitrary digits, Acta Mathematica Hungarica, Volume 125 (2009) no. 1-2, p. 21 | DOI:10.1007/s10474-009-8212-0
de Vries, Martijn; Komornik, Vilmos Unique expansions of real numbers, Advances in Mathematics, Volume 221 (2009) no. 2, pp. 390-427 | DOI:10.1016/j.aim.2008.12.008 | Zbl:1166.11007
Zaïmi, Toufik A remark on the spectra of Pisot numbers, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 347 (2009) no. 1-2, pp. 5-8 | DOI:10.1016/j.crma.2008.11.010 | Zbl:1210.11113
ALLOUCHE, JEAN-PAUL; CLARKE, MATTHEW; SIDOROV, NIKITA Periodic unique beta-expansions: the Sharkovskiĭ ordering, Ergodic Theory and Dynamical Systems, Volume 29 (2009) no. 4, p. 1055 | DOI:10.1017/s0143385708000746
Sidorov, Nikita Expansions in non-integer bases: lower, middle and top orders, Journal of Number Theory, Volume 129 (2009) no. 4, pp. 741-754 | DOI:10.1016/j.jnt.2008.11.003 | Zbl:1230.11090
Benjamini, Itai; Solomyak, Boris Spacings and pair correlations for finite Bernoulli convolutions, Nonlinearity, Volume 22 (2009) no. 2, p. 381 | DOI:10.1088/0951-7715/22/2/008
Allouche, Jean-Paul; Rampersad, Narad; Shallit, Jeffrey Periodicity, repetitions, and orbits of an automatic sequence, Theoretical Computer Science, Volume 410 (2009) no. 30-32, pp. 2795-2803 | DOI:10.1016/j.tcs.2009.02.006 | Zbl:1173.68044
de Vries, Martijn On the number of unique expansions in non-integer bases, Topology and its Applications, Volume 156 (2009) no. 3, pp. 652-657 | DOI:10.1016/j.topol.2008.09.001 | Zbl:1160.11002
Benjamini, Itai; Gurel-Gurevich, Ori; Solomyak, Boris Branching random walk with exponentially decreasing steps, and stochastically self-similar measures, Transactions of the American Mathematical Society, Volume 361 (2009) no. 3, pp. 1625-1643 | DOI:10.1090/s0002-9947-08-04523-6 | Zbl:1162.60023
De Vries, M. A property of algebraic univoque numbers, Acta Mathematica Hungarica, Volume 119 (2008) no. 1-2, pp. 57-62 | DOI:10.1007/s10474-007-6252-x | Zbl:1164.11008
Allouche, Jean-Paul A note on univoque self-Sturmian numbers, RAIRO. Theoretical Informatics and Applications, Volume 42 (2008) no. 4, pp. 659-662 | DOI:10.1051/ita:2007058 | Zbl:1197.11029
Komornik, Vilmos; Loreti, Paola Expansions in Complex Bases, Canadian Mathematical Bulletin, Volume 50 (2007) no. 3, p. 399 | DOI:10.4153/cmb-2007-038-5
Komornik, Vilmos; Loreti, Paola On the topological structure of univoque sets, Journal of Number Theory, Volume 122 (2007) no. 1, pp. 157-183 | DOI:10.1016/j.jnt.2006.04.006 | Zbl:1111.11005
Zaïmi, Toufik Approximation by polynomials with bounded coefficients, Journal of Number Theory, Volume 127 (2007) no. 1, pp. 103-117 | DOI:10.1016/j.jnt.2007.01.014 | Zbl:1166.11032
Dajani, Karma; de Vries, Martijn Invariant densities for random $β$ -expansions, Journal of the European Mathematical Society (JEMS), Volume 9 (2007) no. 1, pp. 157-176 | DOI:10.4171/jems/76 | Zbl:1117.28012
Allouche, Jean-Paul; Frougny, Christiane; Hare, Kevin G. On univoque Pisot numbers, Mathematics of Computation, Volume 76 (2007) no. 259, pp. 1639-1660 | DOI:10.1090/s0025-5718-07-01961-8 | Zbl:1182.11051
Sidorov, Nikita Combinatorics of linear iterated function systems with overlaps, Nonlinearity, Volume 20 (2007) no. 5, p. 1299 | DOI:10.1088/0951-7715/20/5/013
Garth, David; Hare, Kevin G. Comments on the spectra of Pisot numbers, Journal of Number Theory, Volume 121 (2006) no. 2, pp. 187-203 | DOI:10.1016/j.jnt.2006.02.003 | Zbl:1132.11053
Allouche, J.-P.; Shallit, J.; Skordev, G. Self-generating sets, integers with missing blocks, and substitutions, Discrete Mathematics, Volume 292 (2005) no. 1-3, pp. 1-15 | DOI:10.1016/j.disc.2004.12.004 | Zbl:1117.11020
Dajani, Karma; de Vries, Martijn Measures of maximal entropy for random $β$ -expansions, Journal of the European Mathematical Society (JEMS), Volume 7 (2005) no. 1, pp. 51-68 | DOI:10.4171/jems/21 | Zbl:1074.28008
Pedicini, Marco Greedy expansions and sets with deleted digits, Theoretical Computer Science, Volume 332 (2005) no. 1-3, pp. 313-336 | DOI:10.1016/j.tcs.2004.11.002 | Zbl:1080.11009
Zaïmi, Toufik On an approximation property of Pisot numbers. II, Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 1, pp. 239-249 | DOI:10.5802/jtnb.446 | Zbl:1096.11037
Hare, Kevin G. The structure of the spectra of Pisot numbers., Journal of Number Theory, Volume 105 (2004) no. 2, pp. 262-274 | DOI:10.1016/j.jnt.2003.10.001 | Zbl:1045.11074
Broomhead, D S; Sidorov, Nikita Mutual information and capacity of a linear digital channel, Nonlinearity, Volume 17 (2004) no. 6, p. 2203 | DOI:10.1088/0951-7715/17/6/010
Sidorov, Nikita Almost every number has a continuum of $β$ -expansions, American Mathematical Monthly, Volume 110 (2003) no. 9, pp. 838-842 | DOI:10.2307/3647804 | Zbl:1049.11085
Sidorov, N. Universal $β$ -expansions, Periodica Mathematica Hungarica, Volume 47 (2003) no. 1-2, pp. 221-231 | DOI:10.1023/b:mahu.0000010823.98226.4e | Zbl:1049.11009
Sidorov, Nikita Almost Every Number Has a Continuum of β-Expansions, The American Mathematical Monthly, Volume 110 (2003) no. 9, p. 838 | DOI:10.1080/00029890.2003.11920025
Herrmann, Ernst Interval-Filling Sequences Involving Reciprocal Fibonacci Numbers, The Fibonacci Quarterly, Volume 41 (2003) no. 5, p. 441 | DOI:10.1080/00150517.2003.12428556
Zaimi, T. On an approximation property of Pisot numbers, Acta Mathematica Hungarica, Volume 96 (2002) no. 4, p. 309 | DOI:10.1023/a:1019756800260
Borwein, Peter Spectra, Computational Excursions in Analysis and Number Theory (2002), p. 133 | DOI:10.1007/978-0-387-21652-2_16
Dajani, Karma; Kraaikamp, Cor From greedy to lazy expansions and their driving dynamics, Expositiones Mathematicae, Volume 20 (2002) no. 4, pp. 315-327 | DOI:10.1016/s0723-0869(02)80010-x | Zbl:1030.11035
Feng, De-Jun; Wen, Zhiying A property of Pisot numbers, Journal of Number Theory, Volume 97 (2002) no. 2, pp. 305-316 | DOI:10.1016/s0022-314x(02)00013-6 | Zbl:1026.11078
Borwein, Peter; Hare, Kevin G. Some computations on the spectra of Pisot and Salem numbers, Mathematics of Computation, Volume 71 (2002) no. 238, pp. 767-780 | DOI:10.1090/s0025-5718-01-01336-9 | Zbl:1037.11065
Komornik, Vilmos; Loreti, Paola Subexpansions, superexpansions and uniqueness properties in non-integer bases, Periodica Mathematica Hungarica, Volume 44 (2002) no. 2, p. 197 | DOI:10.1023/a:1019696514372
Allouche, J.-P.; Cosnard, M. Non-Integer Bases, Iteration of Continuous Real Maps, and an Arithmetic Self-Similar set, Acta Mathematica Hungarica, Volume 91 (2001) no. 4, p. 325 | DOI:10.1023/a:1010667918943
Komornik, Vilmos; Loreti, Paola; Pedicini, Marco An approximation property of Pisot numbers, Journal of Number Theory, Volume 80 (2000) no. 2, pp. 218-237 | DOI:10.1006/jnth.1999.2456 | Zbl:0962.11034
Komornik, V.; Loreti, P. On the expansions in non-integer bases, Rendiconti di Matematica e delle sue Applicazioni. Serie VII, Volume 19 (1999) no. 4, pp. 615-634 | Zbl:0963.11006
Erdős, Paul; Joó, István; Komornik, Vilmos On the sequence of numbers of the form $ε_{0} + ε_{1} q + \dots + ε_{n} q^{n}$ , $ε \in {0, 1}$ , Acta Arithmetica, Volume 83 (1998) no. 3, pp. 201-210 | DOI:10.4064/aa-83-3-201-210 | Zbl:0896.11006
Erdös, P.; Komornik, V. Developments in Non-Integer Bases, Acta Mathematica Hungarica, Volume 79 (1998) no. 1-2, p. 57 | DOI:10.1023/a:1006557705401
Sidorov, Nikita; Vershik, Anatoly Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems, Monatshefte für Mathematik, Volume 126 (1998) no. 3, pp. 215-261 | DOI:10.1007/bf01367764 | Zbl:0916.28012
Komornik, Vilmos; Loreti, Paola Unique Developments in Non-Integer Bases, The American Mathematical Monthly, Volume 105 (1998) no. 7, p. 636 | DOI:10.1080/00029890.1998.12004937
Joó, I.; Schnitzer, F. J. On some problems concerning expansions by non integer bases, Anzeiger. Abteilung II. Österreichische Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse, Volume 133 (1997), pp. 3-10 | Zbl:0884.11011
Bugeaud, Y. On a property of Pisot numbers and related questions, Acta Mathematica Hungarica, Volume 73 (1996) no. 1-2, p. 33 | DOI:10.1007/bf00058941
Erdős, Paul; Joó, István; Komornik, Vilmos On the number of $q$ -expansions, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, Volume 37 (1994), pp. 109-118 | Zbl:0824.11005
Erdős, P.; Joó, M.; Joó, I. On a problem of Tamas Varga, Bulletin de la Société Mathématique de France, Volume 120 (1992) no. 4, pp. 507-521 | DOI:10.24033/bsmf.2196 | Zbl:0787.11002

Cité par 172 documents. Sources : Crossref, zbMATH