J 2020

Inequalities for entropy, Hausdorff dimension, and Lipschitz constants

ROTH, Samuel Joshua and Zuzana ROTH

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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Poland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

RIV identification code

RIV/47813059:19610/20:A0000081

Organization unit

Mathematical Institute in Opava

UT WoS

000558094200003

Keywords in English

topological entropy; Hausdorff dimension; Lipschitz continuity

Tags

International impact, Reviewed
Změněno: 6/4/2021 13:45, Mgr. Aleš Ryšavý

Abstract

V originále

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.