Time-restricted sensitivity and entropy

TL;DR

This paper explores measure-theoretical and topological restricted sensitivities in dynamical systems, establishing a relationship between restricted sensitivity rates and local entropy for almost every point.

Contribution

It introduces measure-theoretical and topological restricted sensitivities by limiting the first sensitive time and links these sensitivities to local entropy.

Findings

Restricted sensitivity rate equals reciprocal of local entropy for almost every point.

Defines measure-theoretical restricted asymptotic rate in dynamical systems.

Establishes similar results for topological restricted sensitivities.

Abstract

In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dynamical system, we define measure-theoretical restricted asymptotic rate with respect to sensitivity, and obtain that it equal to the reciprocal of the Brin-Katok local entropy for almost every point. For topological version we have similar definitions and conclusions.