Topological pressure, mistake functions and average metric

TL;DR

This paper demonstrates that Pesin pressure under mistake functions and average metrics equals classical Pesin pressure, extending previous results and enhancing understanding of pressure in dynamical systems.

Contribution

It extends the equivalence of Pesin pressure under mistake functions to subsets and average metrics, generalizing prior additive case results.

Findings

Pesin pressure under mistake functions equals classical Pesin pressure

Pesin pressure defined by average metric equals classical Pesin pressure

Extension of previous additive case results

Abstract

In this paper, we showed that the Pesin pressure of any subset under a mistake function is equal to the classical Pesin pressure of the subset in dynamical systems. Our result extended the result of [1] in additive case, which proved the topological pressure of the whole system is self adaptable under a mistake function. As an application, we showed that the Pesin pressure defined by average metric is equal to the classical Pesin pressure.