On translocal entropy functions

In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way that doesn't neglect the initial transient part of an...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Bis, Andrzej, Bruin, Henk
Format: Article
Language:English
Subjects:
Dynamical systems
Entropy
Liapunov exponents
Online Access:Get full text
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Summary:In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way that doesn't neglect the initial transient part of an orbit. We investigate the properties of this ``transient'' local entropy and compute it in terms of Lyapunov exponents for various dynamical systems. We also investigate how this adjustment affects measure-theoretic local (Brin-Katok) entropy.
ISSN:2331-8422