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.