The multifractal spectra for the recurrence rates of beta-transformations

DOI10.1016/j.jmaa.2014.06.051zbMath1347.37031OpenAlexW2051443261MaRDI QIDQ401109

Jung-Chao Ban, Bing Li

Publication date: 26 August 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.06.051

zbMATH Keywords

Hausdorff dimensionrecurrencemultifractalbeta-expansion

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Fractals (28A80) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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Hausdorff dimensions of some irregular sets associated with \(\beta\)-expansions, Zero-one law of Hausdorff dimensions of the recurrent sets, A remark on exceptional sets in Erdös-Rényi limit theorem, Fiber denseness of intermediate β-shifts of finite type, Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps, Approximation orders of real numbers by \(\beta\)-expansions, Finite and infinite arithmetic progressions related to beta-expansion, Dimensions of recurrent sets in \(\beta\)-symbolic dynamics, Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for \(\beta\)-transformation, Unnamed Item, The topological property of the irregular sets on the lengths of basic intervals in beta-expansions, On the distal and asymptotic sets for \(\beta\)-transformations, Distributions of full and non-full words in beta-expansions, THE EXCEPTIONAL SETS ON THE RUN-LENGTH FUNCTION OF β-EXPANSIONS, A CONSTRUCTION OF THE SCRAMBLED SET WITH FULL HAUSDORFF DIMENSION FOR BETA-TRANSFORMATIONS, BADLY APPROXIMABLE AND NONRECURRENT SETS FOR EXPANDING MARKOV MAPS

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