Thermodynamic formalism for general IFS and quantum channels
Visualizar/abrir
Data
2022Autor
Orientador
Co-orientador
Nível acadêmico
Doutorado
Tipo
Abstract
This chapter is part of [BOS22] and 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 s ...
This chapter is part of [BOS22] and 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. ...
Instituição
Universidade Federal do Rio Grande do Sul. Instituto de Matemática e Estatística. Programa de Pós-Graduação em Matemática.
Coleções
-
Ciências Exatas e da Terra (5095)Matemática (362)
Este item está licenciado na Creative Commons License
![](/themes/Mirage2Novo//images/lume/cc.png)