Year: 2013
Type: preprint
Abstract: The goal of this paper is to define and investigate those topological pressures, which is an extension of topological entropy presented by Feng and Huang [13], of continuous transformations. This study reveals the similarity between many known results of topological pressure. More precisely, the investigation of the variational principle is given and related propositions are also described. That is, this paper defines the measure theoretic pressure $P_μ(T,f)$ for any $μ\in{\mathcal M(X)}$, and shows that $P_B(T,f,K)=\sup\bigr\{P_μ(T,f):μ\in{\mathcalM(X)},μ(K)=1\bigr\}$, where $K\subseteq X$ is a non-empty compact subset and $P_B(T,f,K)$ is the Bowen topological pressure on $K$. Furthermore, if $Z\subseteq X$ is an analytic subset, then $P_B(T,f,Z)=\sup\bigr\{P_B(T,f,K):K\subseteq Z\ \text{is compact}\bigr\}$. However, this analysis relies on more techniques of ergodic theory and topological dynamics.
Source: arXiv (Cornell University)
Authors: Tang, Xinjia, Cheng, Wen-Chiao, Zhao, Yun
Institutions: Soochow University, Chinese Culture University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G486622684, G8707143344
OpenAlex ID: W2062902122