Chaotic and topological properties of \(\beta \)-transformations

DOI10.1016/j.jmaa.2011.05.049zbMath1223.37017OpenAlexW1997994909MaRDI QIDQ2275518

Yi-Chiuan Chen, Bing Li

Publication date: 9 August 2011

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.2011.05.049

zbMATH Keywords

chaosHausdorff dimension\(\beta \)-shift

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Symbolic dynamics (37B10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dimension theory of smooth dynamical systems (37C45)

Related Items (13)

Hausdorff dimensions of some irregular sets associated with \(\beta\)-expansions ⋮ The multifractal spectra for the recurrence rates of beta-transformations ⋮ THE DISTAL AND ASYMPTOTIC SETS FOR CONTINUED FRACTIONS ⋮ Approximation orders of real numbers by \(\beta\)-expansions ⋮ Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for \(\beta\)-transformation ⋮ Chaotic and topological properties of continued fractions ⋮ On the distal and asymptotic sets for \(\beta\)-transformations ⋮ A construction of multiply Xiong chaotic set with full topological entropy for \(\beta\)-transformation ⋮ METRIC AND DIMENSIONAL PROPERTIES OF THE BADLY APPROXIMABLE SET FOR BETA-TRANSFORMATIONS ⋮ A CONSTRUCTION OF THE SCRAMBLED SET WITH FULL HAUSDORFF DIMENSION FOR BETA-TRANSFORMATIONS ⋮ Winning property of distal set for β-transformations ⋮ Dynamical Diophantine approximation of beta expansions of formal Laurent series ⋮ BADLY APPROXIMABLE AND NONRECURRENT SETS FOR EXPANDING MARKOV MAPS

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