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Topological Pressure of Discontinuous Potentials of Flow and Variational Principle

Ruolan Xiong

Abstract

Let $X$ be a compact metric space and $Φ=\{\varphi_t\}_{t\in\mathbb{R}}$ be a continuous flow on $X$. We introduce two types of topological pressure for family of discontinuous potentials $a=\{a_t\}_{t>0}$. First, define the topological pressure of family of measurable potentials $a=\{a_t\}_{t>0}$ on a subset $Z$ for flow and proof its invariant principle. The second topological pressure is defined on a invariant subset having a nested family of subsets, we also proof its invariant principle.

Topological Pressure of Discontinuous Potentials of Flow and Variational Principle

Abstract

Let be a compact metric space and be a continuous flow on . We introduce two types of topological pressure for family of discontinuous potentials . First, define the topological pressure of family of measurable potentials on a subset for flow and proof its invariant principle. The second topological pressure is defined on a invariant subset having a nested family of subsets, we also proof its invariant principle.
Paper Structure (4 sections, 146 equations)

This paper contains 4 sections, 146 equations.

Table of Contents

  1. Introduction
  2. Prelimilaries
  3. Variational principle
  4. Topological pressure based on nested set strings

Theorems & Definitions (13)

  • proof
  • proof
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  • ...and 3 more