On ergodic shadowing and specification properties of nonautonomous discrete dynamical systems

Document Type : Research Paper


Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and ;Baluchestan, Zahedan, Iran.


‎We show that a nonautonomous discrete-time dynamical system (NDS) with the ergodic shadowing property is chain mixing‎. ‎As a result‎, ‎it is obtained that a $ k $-periodic NDS with the ergodic shadowing property has the shadowing property‎. In particular‎, ‎any $ k $-periodic NDS on intervals having the ergodic shadowing is Devaney chaotic‎. Additionally‎, ‎we prove that for an equicontinuous NDS with the shadowing property‎, ‎the notions of topologically mixing‎, ‎pseudo-orbital specification‎, ‎weak specification property‎, ‎and ergodic shadowing property are equivalent‎.


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Volume 10, Issue 1
May 2021
Pages 1-10
  • Receive Date: 09 March 2020
  • Revise Date: 11 January 2021
  • Accept Date: 14 January 2021
  • First Publish Date: 16 January 2021