On ergodic shadowing and specification properties of nonautonomous discrete dynamical systems

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.