q-Pressure for Dynamical Systems

• Yun Zhao ^[1] ; Chiyi Luo ^[1] ; Wen-Chiao Cheng ^[2]
  1. [1] Soochow University

     Soochow University

     China

     
  2. [2] Chinese Culture University

     Chinese Culture University

     Taiwán

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Using a (weak) Gibbs measure as the reference measure, this paper introduces the concept of q-topological and q-metric pressure following the approach of Carathéodory construction. Some basic properties of q-pressure are given, including the dependence of q-pressure on the parameter q and a formula for the calculation of q-topological pressure. In particular, a relationship between the q-metric pressure and the local metric pressure is established. Finally, the correlation entropy is defined with respect to any invariant measure, and a relationship is obtained between the correlation entropy and the local metric entropy.

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