Topological pressure of proper map

TL;DR

This paper extends the concept of topological pressure for proper maps on locally compact metric spaces, establishing variational principles and applications based on Carathéodory-Pesin structure theory.

Contribution

It introduces three new notions of topological pressure for proper maps and proves their properties and variational principles, extending classical results.

Findings

Established properties of the new topological pressure notions.

Proved variational principles for proper maps.

Provided applications of the theoretical framework.

Abstract

Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we prove some variational principles and give some applications. These are the extensions of results of Pesin, Takens and Verbiski, etc.