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Nonautonomous Dynamical Systems I: Topological Pressures and Entropies

  • Zhuo Chen [1] ; Jun Jie Miao [2]
    1. [1] East China Normal University

      East China Normal University

      China

    2. [2] China University of Petroleum, Beijing

      China University of Petroleum, Beijing

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • Let X = {Xk }∞ k=0 be a sequence of compact metric spaces Xk and T = {Tk : Xk → Xk+1}∞ k=0 a sequence of continuous mappings. Tk : Xk → Xk+1. The pair (X, T) is called a nonautonomous dynamical system. In this paper, we introduce a variety of topological pressures (Q,Q,P,P,PL,PU,PB and PP) for potentials f = {fk ∈ C(Xk ,R)}∞ k=0 on subsets Z ⊂ X0 which are parallel to those concepts of fractal dimensions, and we provide various key properties that are crucial to the study of nonautonomous dynamical systems. Especially,we obtain the power rules and product rules of these pressures, and we also show they are invariants under equiconjugacies of nonautonomous dynamical systems and equicontinuity on f .

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