Variational Principles for ˛-estimation Topological Pressure

• Yunxiang Xie ^[1] ; Fei Gao ^[1] ; Menglin Ye ^[1]
  1. [1] Nanjing Normal University

     Nanjing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Thieullen defined α-metric as dα n (x, y) = max 0≤i≤n−1 eiαd(T i x, T i y).

    Expanding upon this foundation, we introduce the notations of Pesin-Pitskel αestimation topological pressure and upper capacity α-estimation topological pressure for subsets. We establish Billingsley theorems and variational principles for the PesinPitskel α-topological pressure of compact subsets, in terms of the lower Brin-Katok and Katok α-estimation pressures. Furthermore, by employing techniques from convex analysis and functional analysis, we derive two variational principles involving Borel probability measures and T -invariant measures.

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