The analyticity of a generalized Ruelle’s operator

  • Eduardo Antônio da Silva
  • Raderson Rodrigues da Silva
  • Rafael Rigão SouzaEmail author


In this work we propose a generalization of the concept of Ruelle’s operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle’s operator. Our operator generalizes both the Ruelle operator proposed in [2] and the Perron Frobenius operator defined in [7]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle’s operator and present some examples.


thermodynamic formalism Ruelle’s operator one dimensional lattices a-priori measure analyticity 

Mathematical subject classification

37A60 37A50 82B05 


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Copyright information

© Sociedade Brasileira de Matemática 2014

Authors and Affiliations

  • Eduardo Antônio da Silva
    • 1
  • Raderson Rodrigues da Silva
    • 2
  • Rafael Rigão Souza
    • 3
    Email author
  1. 1.PUC-Rio Departamento de MatemáticaRua Marquês de São VicenteRio de Janeiro, RJBrazil
  2. 2.Departamento de MatemáticaUniversidade de Brasília Campus Universitário Darcy Ribeiro, Asa NorteBrasília, DFBrazil
  3. 3.Departamento de MatemáticaUniversidade Federal do Rio Grande do Sul, UFRGSPorto Alegre, RSBrazil

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