Thermodynamic Formalism for General Iterated Function Systems with Measures

• Jader E. Brasil ^[1] ; Elismar R. Oliveira ^[1] ; Rafael Rigão Souza ^[1]
  1. [1] Instituto de Matemática e Estatística - UFRGS
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • 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 Gâteaux differentiability of the pressure functional.