Relative Time-Restricted Sensitivity and Entropy

Abstract

In this paper, we consider relativization of measure-theoretical- restricted sensitivity. For a given topological dynamical system, we define conditional measure-theoretical-restricted asymptotic rate with respect to sensitivity and obtain that it equals to the reciprocal of the Brin–Katok local entropy for almost every point under the conditional measure.

Keywords

Relative time-restricted sensitivity / Asymptotic rate / Local entropy

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Funding

National Natural Science Foundation of China(11801193)

Fundamental Research Funds for the Central Universities(2020kfyXJJS036)