2020
Inequalities for entropy, Hausdorff dimension, and Lipschitz constants
ROTH, Samuel Joshua and Zuzana ROTHBasic 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
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
References:
Impact factor
Impact factor: 1.023
RIV identification code
RIV/47813059:19610/20:A0000081
Organization unit
Mathematical Institute in Opava
UT WoS
000558094200003
EID Scopus
2-s2.0-85092795587
Keywords in English
topological entropy; Hausdorff dimension; Lipschitz continuity
Tags
Tags
International impact, Reviewed
Changed: 6/4/2021 13:45, Mgr. Aleš Ryšavý
Abstract
In the original language
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.