Title: Ergodic shadowing of non-autonomous discrete-time dynamical systems

Authors: H. Parham; F.H. Ghane; E. Rezaali

Addresses: Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran ' Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran ' Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran

Abstract: The present work is concerned with the ergodic shadowing property of non-autonomous discrete-time dynamical systems. The concept of the ergodic shadowing was introduced by Fakhari and Ghane (2010) for a continuous onto map. Here, we will generalise the notion of ergodic shadowing to non-autonomous discrete-time dynamical systems. We show that every uniformly equicontinuous non-autonomous discrete-time system with the ordinary shadowing and topologically mixing properties enjoys the ergodic shadowing property. Moreover, we define some kind of specification property and investigate its relation to the ergodic shadowing property. Finally, we prove that every uniformly expanding non-autonomous discrete-time system satisfies the ergodic shadowing property.

Keywords: non-autonomous dynamical systems; ergodic shadowing; pseudo orbital specification.

DOI: 10.1504/IJDSDE.2019.10022227

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.2, pp.203 - 212

Received: 29 Nov 2017
Accepted: 18 May 2018

Published online: 27 Jun 2019 *

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