Some results on shadowing and local entropy properties of dynamical systems

TL;DR

This paper investigates the relationship between shadowing properties and local entropy in dynamical systems, providing conditions for entropy points and h-expansiveness, and addressing a question in the field.

Contribution

It offers new necessary and sufficient conditions linking shadowing to entropy properties and presents a counter-example related to h-expansiveness.

Findings

Characterization of entropy points under shadowing

Conditions for h-expansiveness with shadowing and chain transitivity

Counter-example addressing a recent open question

Abstract

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. [Proc. Amer. Math. Soc. 150 (2022), 3369-3378].