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Thermodynamic Formalism for General Iterated Function Systems with Measures
Jader E Brasil1, Elismar R Oliveira1, Rafael Rigão Souza1
1Instituto de Matemática e Estatística - UFRGS, Av. Bento Gonçalves, 9500, Porto Alegre, RS 91509-900 Brazil.
Abstract:
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.
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