Equilibrium stability for non-uniformly hyperbolic systems

被引：5

作者：

Alves, Jose F. ^{[1
]}

Ramos, Vanessa ^{[2
]}

Siqueira, Jaqueline ^{[3
]}

机构：

[1] Univ Porto, Ctr Matemat, Rua Campo Alegre 687, P-4169007 Porto, Portugal

[2] UFMA, Ctr Ciencias Exatas & Tecnol, Av Portugueses 1966, BR-65080805 Bacanga, Sao Luis, Brazil

[3] PUC Rio, Dept Matemat, Marques de Sao Vicente 225, BR-22545390 Gavea, RJ, Brazil

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2019年 / 39卷

基金：

巴西圣保罗研究基金会;

关键词：

VARIATIONAL PRINCIPLE; ROBUST CLASSES; SRB MEASURES; STATES; ENTROPY; HORSESHOES; UNIQUENESS; EXISTENCE; FORMALISM; MAPS;

D O I：

10.1017/etds.2017.138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the topological pressure is continuous as a function of the dynamics and the potential. We also prove the existence of finitely many ergodic equilibrium states for non-uniformly hyperbolic skew products and hyperbolic Holder continuous potentials. Finally, we show that these equilibrium states vary continuously in the weak* topology within such systems.

引用

页码：2619 / 2642

页数：24

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