Characterization of the unique expansions 1=∑i=1∞q-ni and related problems
Bulletin de la Société Mathématique de France, Tome 118 (1990) no. 3, pp. 377-390. 
@article{BSMF_1990__118_3_377_0,
     author = {Erd\"os, P\'al and Jo\'o, Istv\'a n 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://www.numdam.org/articles/10.24033/bsmf.2151/}
}
TY  - JOUR
AU  - Erdös, Pál
AU  - Joó, Istvá n
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://www.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, Istvá n
%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://www.numdam.org/articles/10.24033/bsmf.2151/
%R 10.24033/bsmf.2151
%G en
%F BSMF_1990__118_3_377_0
Erdös, Pál; Joó, Istvá n; 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. https://www.numdam.org/articles/10.24033/bsmf.2151/

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

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

[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
  • Hu, Yuecai; Barrera, Rafael Alcaraz; Zou, Yuru Topological and dimensional properties of univoque bases in double-base expansions, Topology and its Applications, Volume 366 (2025), p. 109294 | DOI:10.1016/j.topol.2025.109294
  • Lai, A. C.; Loreti, P. Optimal expansions of Kakeya sequences, Acta Mathematica Hungarica, Volume 174 (2024) no. 1, p. 1 | DOI:10.1007/s10474-024-01453-8
  • 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
  • Kong, Derong; Sun, Beibei Projections of four corner Cantor set: Total self-similarity, spectrum and unique codings, Indagationes Mathematicae (2024) | DOI:10.1016/j.indag.2024.08.006
  • Kalle, Charlene; Verbitskiy, Evgeny; Zeegers, Benthen Pseudo-random number generation with β-encoders, International Journal of Mathematics for Industry, Volume 16 (2024) no. 01 | DOI:10.1142/s2661335224500266
  • Komornik, Vilmos; Loreti, Paola; Pedicini, Marco A quasi-ergodic approach to non-integer base expansions, Journal of Number Theory, Volume 254 (2024), p. 146 | DOI:10.1016/j.jnt.2023.07.009
  • Charlier, Émilie; Cisternino, Célia; Kreczman, Savinien On periodic alternate base expansions, Journal of Number Theory, Volume 254 (2024), p. 184 | DOI:10.1016/j.jnt.2023.07.008
  • Li, Rao; Lü, Fan Run-length function of the beta-expansion of a fixed real number, Journal of Number Theory, Volume 256 (2024), p. 55 | DOI:10.1016/j.jnt.2023.09.002
  • Komornik, Vilmos; Steiner, Wolfgang; Zou, Yuru Unique double base expansions, Monatshefte für Mathematik, Volume 204 (2024) no. 3, p. 513 | DOI:10.1007/s00605-024-01973-z
  • 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 | DOI:10.1007/s40993-024-00558-x
  • Li, Yao-Qiang Expansions of generalized Thue-Morse numbers, Advances in Applied Mathematics, Volume 143 (2023), p. 102456 | DOI:10.1016/j.aam.2022.102456
  • 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, p. 3861 | DOI:10.1017/etds.2022.79
  • CHARLIER, ÉMILIE; CISTERNINO, CÉLIA; DAJANI, KARMA Dynamical behavior of alternate base expansions, Ergodic Theory and Dynamical Systems, Volume 43 (2023) no. 3, p. 827 | DOI:10.1017/etds.2021.161
  • Mackenzie, Andrew; Komornik, Vilmos Fairly taking turns, Games and Economic Behavior, Volume 142 (2023), p. 743 | DOI:10.1016/j.geb.2023.09.005
  • 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), p. 46 | DOI:10.1016/j.jnt.2022.12.005
  • Li, Yao-Qiang Bifurcations of digit frequencies in unique expansions, Journal of Number Theory, Volume 248 (2023), p. 420 | DOI:10.1016/j.jnt.2022.12.008
  • Charlier, Émilie; Cisternino, Célia; Masáková, Zuzana; Pelantová, Edita Spectrum, algebraicity and normalization in alternate bases, Journal of Number Theory, Volume 249 (2023), p. 470 | DOI:10.1016/j.jnt.2023.02.012
  • 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, p. 481 | DOI:10.1007/s10474-022-01231-4
  • Vargas, Victor On involution kernels and large deviations principles on β-shifts, Discrete and Continuous Dynamical Systems, Volume 42 (2022) no. 6, p. 2699 | DOI:10.3934/dcds.2021208
  • KALLE, CHARLENE; MAGGIONI, MARTA Invariant densities for random systems of the interval, Ergodic Theory and Dynamical Systems, Volume 42 (2022) no. 1, p. 141 | DOI:10.1017/etds.2020.127
  • Zou, Yuru; Lu, Jian; Komornik, Vilmos Hausdorff dimension of multiple expansions, Journal of Number Theory, Volume 233 (2022), p. 198 | DOI:10.1016/j.jnt.2021.06.009
  • de Vries, Martijn; Komornik, Vilmos; Loreti, Paola Topology of univoque sets in real base expansions, Topology and its Applications, Volume 312 (2022), p. 108085 | DOI:10.1016/j.topol.2022.108085
  • Li, Y.-Q. Expansions in multiple bases, Acta Mathematica Hungarica, Volume 163 (2021) no. 2, p. 576 | DOI:10.1007/s10474-020-01094-7
  • 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. 102146 | DOI:10.1016/j.aam.2020.102146
  • Li, Yao-Qiang Hausdorff dimension of frequency sets of univoque sequences, Dynamical Systems, Volume 36 (2021) no. 2, p. 340 | DOI:10.1080/14689367.2021.1905778
  • ALLAART, PIETER; KONG, DERONG Relative bifurcation sets and the local dimension of univoque bases, Ergodic Theory and Dynamical Systems, Volume 41 (2021) no. 8, p. 2241 | DOI:10.1017/etds.2020.38
  • BARRERA, RAFAEL ALCARAZ On the specification property and synchronization of uniqueq-expansions, Ergodic Theory and Dynamical Systems, Volume 41 (2021) no. 9, p. 2659 | DOI:10.1017/etds.2020.55
  • Vávra, Tomáš Periodic representations in Salem bases, Israel Journal of Mathematics, Volume 242 (2021) no. 1, p. 83 | DOI:10.1007/s11856-021-2123-3
  • Neunhäuserer, Jörg Non-uniform Expansions of Real Numbers, Mediterranean Journal of Mathematics, Volume 18 (2021) no. 2 | DOI:10.1007/s00009-021-01723-7
  • 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, p. 2667 | DOI:10.1007/s11425-020-1763-5
  • 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, p. 6201 | DOI:10.1090/tran/8332
  • Li, Y.-Q. Digit frequencies of beta-expansions, Acta Mathematica Hungarica, Volume 162 (2020) no. 2, p. 403 | DOI:10.1007/s10474-020-01032-7
  • 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. 102103 | DOI:10.1016/j.aam.2020.102103
  • Zhao, Bing; Ren, Xiaomin; Zhu, Jiali; Jiang, Kan Arithmetic on self-similar sets, Indagationes Mathematicae, Volume 31 (2020) no. 4, p. 595 | DOI:10.1016/j.indag.2020.05.003
  • 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
  • Dajani, Karma; Kong, Derong; Yao, Yuanyuan On the structure of λ-Cantor set with overlaps, Advances in Applied Mathematics, Volume 108 (2019), p. 97 | DOI:10.1016/j.aam.2019.04.003
  • Allaart, Pieter; Kong, Derong On the continuity of the Hausdorff dimension of the univoque set, Advances in Mathematics, Volume 354 (2019), p. 106729 | DOI:10.1016/j.aim.2019.106729
  • KWON, DOYONG Sturmian words and Cantor sets arising from unique expansions over ternary alphabets, Ergodic Theory and Dynamical Systems, Volume 39 (2019) no. 10, p. 2827 | DOI:10.1017/etds.2017.136
  • SUZUKI, SHINTARO Invariant density functions of random -transformations, Ergodic Theory and Dynamical Systems, Volume 39 (2019) no. 4, p. 1099 | DOI:10.1017/etds.2017.64
  • Komornik, Vilmos; Kong, Derong Bases in which some numbers have exactly two expansions, Journal of Number Theory, Volume 195 (2019), p. 226 | DOI:10.1016/j.jnt.2018.06.004
  • Tan, Bo; Zhang, Liling On small bases which admit countably many expansions with multiple digits, Journal of Number Theory, Volume 196 (2019), p. 87 | DOI:10.1016/j.jnt.2018.09.021
  • BAKER, SIMON; KONG, DERONG Numbers with simply normal β-expansions, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 167 (2019) no. 01, p. 171 | DOI:10.1017/s0305004118000270
  • Dajani, Karma; Jiang, Kan; Kong, Derong; Li, Wenxia Multiple expansions of real numbers with digits set {0,1,q} 0 , 1 , q, Mathematische Zeitschrift, Volume 291 (2019) no. 3-4, p. 1605 | DOI:10.1007/s00209-018-2123-0
  • Šíma, Jiří Subrecursive neural networks, Neural Networks, Volume 116 (2019), p. 208 | DOI:10.1016/j.neunet.2019.04.019
  • Bandt, Christoph Finite orbits in multivalued maps and Bernoulli convolutions, Advances in Mathematics, Volume 324 (2018), p. 437 | DOI:10.1016/j.aim.2017.11.011
  • 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, p. 207 | DOI:10.1007/s10476-018-0206-0
  • Hare, Kevin G.; Masáková, Zuzana; Vávra, Tomáš On the spectra of Pisot-cyclotomic numbers, Letters in Mathematical Physics, Volume 108 (2018) no. 7, p. 1729 | DOI:10.1007/s11005-018-1053-4
  • Šíma, Jiří; Savický, Petr Quasi-periodic β-expansions and cut languages, Theoretical Computer Science, Volume 720 (2018), p. 1 | DOI:10.1016/j.tcs.2018.02.028
  • 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 (2018) no. 5, p. 3209 | DOI:10.1090/tran/7370
  • 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, p. 25 | DOI:10.1007/s10474-017-0706-6
  • Baiocchi, C.; Komornik, V.; Loreti, P. Cantor type functions in non-integer bases, Acta Mathematica Hungarica, Volume 153 (2017) no. 1, p. 83 | DOI:10.1007/s10474-017-0732-4
  • 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), p. 165 | DOI:10.1016/j.aim.2016.03.047
  • Allaart, Pieter C. On univoque and strongly univoque sets, Advances in Mathematics, Volume 308 (2017), p. 575 | DOI:10.1016/j.aim.2016.12.029
  • Baker, Simon; Steiner, Wolfgang On the regularity of the generalised golden ratio function, Bulletin of the London Mathematical Society, Volume 49 (2017) no. 1, p. 58 | DOI:10.1112/blms.12002
  • Cao, Chunyun; Chen, Yuanhong The run-length function of the β-expansion of the unit, Journal of Number Theory, Volume 177 (2017), p. 248 | DOI:10.1016/j.jnt.2017.01.015
  • Kong, Derong; Li, Wenxia; Lü, Fan; de Vries, Martijn Univoque bases and Hausdorff dimension, Monatshefte für Mathematik, Volume 184 (2017) no. 3, p. 443 | DOI:10.1007/s00605-017-1047-9
  • Jiang, Kan; Dajani, Karma Subshifts of finite type and self-similar sets, Nonlinearity, Volume 30 (2017) no. 2, p. 659 | DOI:10.1088/1361-6544/aa53c7
  • 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 (2017), p. 39 | DOI:10.1007/978-3-319-57805-7_2
  • 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, p. 194 | DOI:10.1007/s10474-016-0637-7
  • 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), p. 134 | DOI:10.1016/j.jnt.2015.06.017
  • Hu, Hui; Tong, Xin; Yu, Yueli On consecutive 0 digits in the β-expansion of 1, Journal of Number Theory, Volume 166 (2016), p. 219 | DOI:10.1016/j.jnt.2016.02.019
  • 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
  • Zou, Yuru; Wang, Lijin; Lu, Jian; Baker, Simon ON SMALL BASES FOR WHICH 1 HAS COUNTABLY MANY EXPANSIONS, Mathematika, Volume 62 (2016) no. 2, p. 362 | DOI:10.1112/s002557931500025x
  • 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, p. 1 | DOI:10.1007/s00605-015-0755-2
  • 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), p. 117 | DOI:10.1016/j.topol.2016.01.023
  • Boyland, Philip; de Carvalho, André; Hall, Toby On digit frequencies in 𝛽-expansions, Transactions of the American Mathematical Society, Volume 368 (2016) no. 12, p. 8633 | DOI:10.1090/tran/6617
  • Baker, Simon On small bases which admit countably many expansions, Journal of Number Theory, Volume 147 (2015), p. 515 | DOI:10.1016/j.jnt.2014.08.003
  • Masáková, Zuzana; Pastirčáková, Kateřina; Pelantová, Edita Description of spectra of quadratic Pisot units, Journal of Number Theory, Volume 150 (2015), p. 168 | DOI:10.1016/j.jnt.2014.11.011
  • 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, Simon On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions, Acta Mathematica Hungarica, Volume 142 (2014) no. 1, p. 95 | DOI:10.1007/s10474-013-0366-0
  • Vince, Andrew A combinatorial approach to binary positional number systems, Acta Mathematica Hungarica, Volume 143 (2014) no. 1, p. 138 | DOI:10.1007/s10474-013-0387-8
  • Barrera, Rafael Alcaraz Topological and ergodic properties of symmetric sub-shifts, Discrete and Continuous Dynamical Systems, Volume 34 (2014) no. 11, p. 4459 | DOI:10.3934/dcds.2014.34.4459
  • Masáková, Zuzana; Pelantová, Edita Optimal number representations in negative base, Acta Mathematica Hungarica, Volume 140 (2013) no. 4, p. 329 | DOI:10.1007/s10474-013-0336-6
  • 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, p. 375 | DOI:10.1016/j.jnt.2012.07.015
  • 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: An Interdisciplinary Journal of Nonlinear Science, Volume 22 (2012) no. 4 | DOI:10.1063/1.4758813
  • 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, p. 536 | DOI:10.1016/j.dam.2011.10.029
  • 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, p. 371 | DOI:10.1112/s0025579312000083
  • 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
  • Lai, Anna Chiara Minimal unique expansions with digits in ternary alphabets, Indagationes Mathematicae, Volume 21 (2011) no. 1-2, p. 1 | DOI:10.1016/j.indag.2010.11.001
  • 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, Volume 348 (2010) no. 3-4, p. 121 | DOI:10.1016/j.crma.2010.01.016
  • Komornik, Vilmos; Loreti, Paola Universal Expansions in Negative and Complex Bases, Integers, Volume 10 (2010) no. 6 | DOI:10.1515/integ.2010.050
  • 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 (2010), p. 383 | DOI:10.1007/978-0-8176-4888-6_24
  • 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, p. 390 | DOI:10.1016/j.aim.2008.12.008
  • 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, p. 741 | DOI:10.1016/j.jnt.2008.11.003
  • 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, p. 2795 | DOI:10.1016/j.tcs.2009.02.006
  • de Vries, Martijn On the number of unique expansions in non-integer bases, Topology and its Applications, Volume 156 (2009) no. 3, p. 652 | DOI:10.1016/j.topol.2008.09.001
  • de Vries, M. A property of algebraic univoque numbers, Acta Mathematica Hungarica, Volume 119 (2008) no. 1-2, p. 57 | DOI:10.1007/s10474-007-6252-x
  • Zaïmi, Toufik Une remarque sur le spectre des nombres de Pisot, Comptes Rendus. Mathématique, Volume 347 (2008) no. 1-2, p. 5 | DOI:10.1016/j.crma.2008.11.010
  • Allouche, Jean-Paul A note on univoque self-Sturmian numbers, RAIRO - Theoretical Informatics and Applications, Volume 42 (2008) no. 4, p. 659 | DOI:10.1051/ita:2007058
  • 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, p. 157 | DOI:10.1016/j.jnt.2006.04.006
  • Zaimi, Toufik Approximation by polynomials with bounded coefficients, Journal of Number Theory, Volume 127 (2007) no. 1, p. 103 | DOI:10.1016/j.jnt.2007.01.014
  • 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, p. 187 | DOI:10.1016/j.jnt.2006.02.003
  • Allouche, J.-P.; Shallit, J.; Skordev, G. Self-generating sets, integers with missing blocks, and substitutions, Discrete Mathematics, Volume 292 (2005) no. 1-3, p. 1 | DOI:10.1016/j.disc.2004.12.004
  • Pedicini, Marco Greedy expansions and sets with deleted digits, Theoretical Computer Science, Volume 332 (2005) no. 1-3, p. 313 | DOI:10.1016/j.tcs.2004.11.002
  • Hare, Kevin G. The structure of the spectra of Pisot numbers, Journal of Number Theory, Volume 105 (2004) no. 2, p. 262 | DOI:10.1016/j.jnt.2003.10.001
  • 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, 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
  • 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, p. 315 | DOI:10.1016/s0723-0869(02)80010-x
  • Feng, De-Jun; Wen, Zhi-Ying A property of Pisot numbers, Journal of Number Theory, Volume 97 (2002) no. 2, p. 305 | DOI:10.1016/s0022-314x(02)00013-6
  • Komornik, Vilmos; Loreti, Paola; Pedicini, Marco An Approximation Property of Pisot Numbers, Journal of Number Theory, Volume 80 (2000) no. 2, p. 218 | DOI:10.1006/jnth.1999.2456
  • Sidorov, Nikita; Vershik, Anatoly Ergodic properties of the Erd�s measure, the entropy of the goldenshift, and related problems, Monatshefte f�r Mathematik, Volume 126 (1998) no. 3, p. 215 | DOI:10.1007/bf01367764
  • 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
  • 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

Cité par 136 documents. Sources : Crossref