ROTH, Samuel Joshua and Zuzana ROTH. Inequalities for entropy, Hausdorff dimension, and Lipschitz constants. Studia Mathematica. WARSZAWA: POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, vol. 250, No 3, p. 253-264. ISSN 0039-3223. doi:10.4064/sm180705-2-11. 2020.
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Basic information
Original name Inequalities for entropy, Hausdorff dimension, and Lipschitz constants
Authors ROTH, Samuel Joshua (840 United States of America, belonging to the institution) and Zuzana ROTH (703 Slovakia, belonging to the institution).
Edition Studia Mathematica, WARSZAWA, POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, 2020, 0039-3223.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Poland
Confidentiality degree is not subject to a state or trade secret
WWW Studia Mathematica
RIV identification code RIV/47813059:19610/20:A0000081
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.4064/sm180705-2-11
UT WoS 000558094200003
Keywords in English topological entropy; Hausdorff dimension; Lipschitz continuity
Tags MÚ, SGS-16-2016
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 13:45.
Abstract
We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lower bound for topological entropy in terms of the resulting Hausdorff dimensions and Lipschitz constants. This reverses an old inequality of Dai, Zhou, and Geng and leads to a short proof of a well-known theorem on expansive mappings. It also suggests a new invariant of topological conjugacy for dynamical systems on compact metric spaces.
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