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Continuous self maps of R pressure and R pressure measure topology

Author: ChenYaMing
Tutor: ChenErCai
School: Nanjing Normal University
Course: Basic mathematics
Keywords: topological pressure measure-theoretic r-pressure topological r-pressure variational principle
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 3
Quote: 0
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Abstract


In this thesis, We introduce the concepts of measure-theoretic r-pressure and topological r-pressure of a continuous map on a compact metric space, and discusses some important properties. Meanwhile, we get the results as follows:Measure-theoretic pressure is the limit of measure-theoretic r-pressure and topological pres-sure is the limit of topological r-pressure (r→0). The paper is organized as follows:In chapter one, we mainly review the development of the entropy and the topo-logical pressure.In chapter two, we recall some classical definitions and lemmas in topological dynamical system and ergodic theory.In chapter three, we introduce the notions of measure-theoretic r-pressure and topological r-pressure, discuss some properties and prove both convergence theorems.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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