arXiv subjects

J. Nazarian Sarkooh

Publications and source records attributed to J. Nazarian Sarkooh.

2 recordsLinked to original sources

arXiv2019

Specification and Thermodynamic Properties of Topological Time-Dependent Dynamical Systems

This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical system given by a sequence of surjective continuous self maps of a compact metric space with the specification property has positive topological entropy and all points are entropy point. In particular, it is proved that these systems are topologically chaotic. We will treat the dynamics of uniformly Ruelle-expanding time-dependent dynamical systems on compact metric spaces and provide some sufficient conditions that these systems have the specification property. Consequently, we conclude that these systems have positive topological entropy. This extends a result of Kawan \cite{K2}, corresponding to the case when the expanding maps are smooth, to the more general case of expanding maps. Additionally, we study the topological pressure of time-dependent dynamical systems. We obtain conditions under which the topological entropy and topological pressure of any continuous potential can be computed as a limit at a definite size scale. Finally, we study the Lipschitz regularity of the topological pressure function for expansive (uniformly Ruelle-expanding) time-dependent dynamical systems on compact metric spaces.

math.DS↗

arXiv2019

On topological entropy and topological pressure of non-autonomous iterated function systems

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given \cite{LGMU} by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the $\ast$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the $\ast$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and $\ast$-expansive properties.

math.DS↗