Thermodynamic Formalism for General Iterated Function Systems with Measures

被引：5

作者：

Brasil, Jader E. ^{[1
]}

Oliveira, Elismar R. ^{[1
]}

Souza, Rafael Rigao ^{[1
]}

机构：

[1] Univ Fed Rio Grande do Sul, Inst Matemat & Estat, Ave Bento Goncalves 9500, BR-91509900 Porto Alegre, RS, Brazil

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2023年 / 22卷 / 01期

关键词：

Iterated function system; Thermodynamic formalism; Ergodic theory; Transfer operator; Entropy; Pressure; Equilibrium states; INVARIANT-MEASURES; ATTRACTORS; ENTROPY; THEOREM; SETS;

D O I：

10.1007/s12346-022-00722-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential. A definition of equilibrium state is then natural and we prove its existence for any continuous potential. We show, in this setting, a uniqueness result for the equilibrium state requiring only the Gateaux differentiability of the pressure functional.

引用

页数：26

共 33 条

[1] A variational principle for the specific entropy for symbolic systems with uncountable alphabets [J].