on the shadowing property of nonautonomous discrete systems

On the shadowing property of nonautonomous discrete systems

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.

On the Notion of Fuzzy Shadowing Property

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

On Periodic Shadowing Property

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

On ergodicity of systems with the asymptotic average shadowing property

On Nonautonomous Discrete Dynamical Systems Driven by Means

We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): yj(n+ 1) = Fj(n, y(n)); j = 1, . . . ,k, n = 0,1,2, . . . , where y(n) = (y1(n), . . . , yk(n)) ∈ Rk, y(0) = x, and Fj(n,·) is a mean of k (≥ 2) positive real numbers, that is, a real-valued function satisfying the internality property min(x)≤ ...

Limit Shadowing Property

In this paper pseudoorbits of discrete dynamical systems are considered such that the one{step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error ...