A Billingsley-type theorem for the pressure of an action of an amenable group

Xiaojun Huang; Yuan Lian; Changrong Zhu

doi:10.3934/dcds.2019040

Article Contents

2019, Volume 39, Issue 2: 959-993. Doi: 10.3934/dcds.2019040

This issue Previous Article Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response Next Article Topological entropy of free semigroup actions for noncompact sets

A Billingsley-type theorem for the pressure of an action of an amenable group

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

* Corresponding author
* Corresponding author

Received: March 2018

Revised: August 2018

Published: February 2019

The research was supported by NSF of China (No. 11671057, No. 11471318, No. 11671058) and the Fundamental Research Funds for the Central Universities (No. 2018CDQYST0023)

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Abstract

This paper extends the definition of Bowen topological entropy of subsets to Pesin-Pitskel topological pressure for the continuous action of amenable groups on a compact metric space. We introduce the local measure theoretic pressure of subsets and investigate the relation between local measure theoretic pressure of Borel probability measures and Pesin-Pitskel topological pressure on an arbitrary subset of a compact metric space.

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Mathematics Subject Classification: 37A35, 37B40.

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References

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