Multi-transitivity in non-autonomous discrete systems

Abstract

We introduce and study the notions of multi-transitivity and thick transitivity for non-autonomous discrete dynamical systems. We obtain a sufficient condition under which in minimal non-autonomous discrete dynamical systems, multi-transitivity, thick transitivity and weakly mixing of all orders are equivalent. Counterexamples are constructed justifying that certain results related to above concepts which are true in autonomous discrete dynamical systems need not be true in non-autonomous discrete dynamical systems.