On Schmidt's game and the set of points with non-dense orbits under a class of expanding maps

DOI10.1016/J.JMAA.2014.04.026zbMath1345.37038OpenAlexW2084542492MaRDI QIDQ488534

Yueli Yu, Hui Hu

Publication date: 26 January 2015

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.2014.04.026

zbMATH Keywords

Schmidt's gamenon-dense orbitbeta transformationGauss transformation

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving maps of the interval (37E05)

Related Items (12)

MEAN LI–YORKE CHAOTIC SET WITH FULL HAUSDORFF DIMENSION FOR CONTINUED FRACTIONS ⋮ Intermediate \(\beta\)-shifts as greedy \(\beta\)-shifts with a hole ⋮ THE DISTAL AND ASYMPTOTIC SETS FOR CONTINUED FRACTIONS ⋮ Schmidt’s game and nonuniformly expanding interval maps ⋮ Chaotic and topological properties of continued fractions ⋮ The Hausdorff dimension of multiply Xiong chaotic sets ⋮ Winning property of distal set for β-transformations ⋮ Tanaka–Ito α-continued fractions and matching ⋮ Limit theorems for sums of products of consecutive partial quotients of continued fractions ⋮ Non-dense orbits on homogeneous spaces and applications to geometry and number theory ⋮ Non-dense orbits of systems with the approximate product property ⋮ BADLY APPROXIMABLE AND NONRECURRENT SETS FOR EXPANDING MARKOV MAPS

Cites Work

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• Representations of real numbers by infinite series
• Beta-expansion and continued fraction expansion
• Schmidt’s game, fractals, and orbits of toral endomorphisms
• Simultaneously non-dense orbits under different expanding maps
• Dimension of countable intersections of some sets arising in expansions in non-integer bases
• On theβ-expansions of real numbers
• Schmidt games and Markov partitions
• On orbits of endomorphisms of tori and the Schmidt game
• Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists
• On Badly Approximable Numbers and Certain Games

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