Topological pressure of a factor map for nonautonomous dynamical systems. (English) Zbl 1523.37027
Summary: Let \((X,d)\) be a compact metric space and \(\{ f_i\}^{\infty}_{i=1}\) be a sequence of continuous maps from \(X\) to itself. Denote by \(f_{1,\infty}\) the sequence \(\{f_i\}^{\infty}_{i=1}\) and by \((X,d,f_{1,\infty})\) the induced nonautonomous dynamical system. In this paper, we give the definitions of upper capacity topological pressure and Pesin-Pitskel topological pressure on a noncompact subset for nonautonomous dynamical systems from the dimension theory. Moreover, we propose the equivalent definition of Pesin-Pitskel topological pressure and investigate some properties of topological pressure. In contrast to Bowen’s inequality, we discuss a relation for two topological pressures and establish an inequality formula for two topological pressures with a factor map of nonautonomous dynamical systems.
MSC:
| 37B40 | Topological entropy |
| 37B65 | Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems |
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