We compute a lower bound of Billingsley–Hausdorff dimension, defined by Gibbs measure, of the level set related to Birkhoff average in the countable symbolic space .
Révisé le :
Accepté le :
Publié le :
@article{CRMATH_2020__358_3_255_0,
author = {Attia, Najmeddine and Selmi, Bilel},
title = {On the {Billingsley} dimension of {Birkhoff} average in the countable symbolic space},
journal = {Comptes Rendus. Math\'ematique},
pages = {255--265},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {3},
year = {2020},
doi = {10.5802/crmath.21},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.21/}
}
TY - JOUR AU - Attia, Najmeddine AU - Selmi, Bilel TI - On the Billingsley dimension of Birkhoff average in the countable symbolic space JO - Comptes Rendus. Mathématique PY - 2020 SP - 255 EP - 265 VL - 358 IS - 3 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.21/ DO - 10.5802/crmath.21 LA - en ID - CRMATH_2020__358_3_255_0 ER -
%0 Journal Article %A Attia, Najmeddine %A Selmi, Bilel %T On the Billingsley dimension of Birkhoff average in the countable symbolic space %J Comptes Rendus. Mathématique %D 2020 %P 255-265 %V 358 %N 3 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.21/ %R 10.5802/crmath.21 %G en %F CRMATH_2020__358_3_255_0
Attia, Najmeddine; Selmi, Bilel. On the Billingsley dimension of Birkhoff average in the countable symbolic space. Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 255-265. doi : 10.5802/crmath.21. http://www.numdam.org/articles/10.5802/crmath.21/
[1] Multifractal analysis of Birkhoff averages on ‘self-affine’ symbolic spaces, Nonlinearity (2008), pp. 2409-2425 | DOI | MR | Zbl
[2] Full shifts and irregular sets, São Paulo J. Math. Sci., Volume 6 (2012) no. 2, pp. 135-143 | DOI | MR | Zbl
[3] Ergodic theory and information, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, 1965 | Zbl
[4] Topological entropy for noncompact set, Trans. Am. Math. Soc., Volume 184 (1973), pp. 125-136 | DOI | MR | Zbl
[5] Billingsley Dimension in probability spaces, Lecture Notes in Mathematics, 892, Springer, 1981 | MR | Zbl
[6] Thermodynamic approach to multifractal analysis, Ergodic Theory Dyn. Syst., Volume 34 (2014) no. 5, pp. 1409-1450 | DOI | MR | Zbl
[7] Multifractal Analysis of The New Level sets (2015) (https://arxiv.org/abs/1510.06514v1)
[8] On the Distribution of Long-Term Time Averages on Symbolic Space, J. Stat. Phys., Volume 99 (2000) no. 3-4, pp. 813-856 | DOI | MR | Zbl
[9] Recurrence, dimension and entropy, J. Lond. Math. Soc., Volume 64 (2001) no. 1, pp. 229-244 | DOI | MR | Zbl
[10] Multifractal analysis for expanding interval maps with infinitely many branches, Trans. Am. Math. Soc., Volume 367 (2015) no. 3, pp. 1847-1870 | DOI | MR | Zbl
[11] Generic points of shift-invariant measures in the countable symbolic space, Math. Proc. Camb. Philos. Soc., Volume 166 (2019) no. 2, pp. 381-413 | DOI | MR | Zbl
[12] On the frequency of partial quotients of regular continued fractions, Math. Proc. Camb. Philos. Soc., Volume 148 (2010) no. 1, pp. 179-192 | DOI | MR | Zbl
[13] Level sets of multiple ergodic averages, Monatsh. Math., Volume 168 (2012) no. 1, pp. 17-26 | DOI | MR | Zbl
[14] Dimension of Besicovitch-Eggleston sets in countable symbolic space, Nonlinearity, Volume 23 (2010) no. 5, pp. 1185-1197 | DOI | MR | Zbl
[15] Generic points in systems of specification and Banach valued Birkhoff ergodic average, Discrete Contin. Dyn. Syst., Volume 21 (2008) no. 4, pp. 1103-1128 | DOI | MR | Zbl
[16] On Khintchine exponents and Lyapunov exponents of continued fractions, Ergodic Theory Dyn. Syst., Volume 29 (2009) no. 1, pp. 73-109 | DOI | MR | Zbl
[17] On fast Birkhoff averaging, Math. Proc. Camb. Philos. Soc., Volume 135 (2003) no. 3, pp. 443-467 | DOI | MR | Zbl
[18] Ergodic Limits on the Conformal Repellers, Adv. Math., Volume 169 (2002) no. 1, pp. 58-91 | DOI | MR | Zbl
[19] Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages, Ergodic Theory Dyn. Syst., Volume 29 (2009) no. 3, pp. 885-918 | DOI | MR | Zbl
[20] On the interplay between measurable and topological dynamics, Handbook of dynamical systems. Volume 1B, Volume 1, Elsevier, 2006, pp. 597-648 | Zbl
[21] Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets, J. Fractal Geom., Volume 1 (2014) no. 1, pp. 83-152 | DOI | MR | Zbl
[22] On a lemma of Bowen, Acta Math. Sci., Ser. B, Engl. Ed., Volume 34 (2014) no. 3, pp. 932-940 | MR | Zbl
[23] Bowen lemma in the countable symbolic space, Entropy, Volume 19 (2017) no. 10, p. 532 | DOI | MR
[24] Dimension of some non-normal continued fraction sets, Math. Proc. Camb. Philos. Soc., Volume 145 (2008) no. 1, pp. 215-225 | DOI | MR | Zbl
[25] The multifractal analysis of Birkhoff averages and large deviations, Global analysis of dynamical systems, Institute of Physics Publishing, 2001, pp. 419-431 | Zbl
[26] Large deviations estimates for dynamical systems without the specification property, Nonlinearity, Volume 18 (2005) no. 1, pp. 237-261 | DOI | MR | Zbl
[27] Thermodynamic formalism for countable Markov shifts, Ergodic Theory Dyn. Syst., Volume 19 (1999) no. 6, pp. 1565-1593 | DOI | MR | Zbl
[28] Existence of Gibbs measures for countable Markov shifts, Proc. Am. Math. Soc., Volume 131 (2003) no. 6, p. 1751-1558 | DOI | MR | Zbl
[29] Lecture notes on thermodynamic formalism for topological markov shifts (2009) (http://www.wisdom.weizmann.ac.il/~sarigo/TDFnotes.pdf)
Cité par Sources :
