Specification properties for non-autonomous discrete systems

Abstract

In this paper notions of strong specification property and quasi-weak specification property for non-autonomous discrete systems are introduced and studied. It is shown that these properties are dynamical properties and are preserved under finite product. It is proved that a $k$-periodic non-autonomous system on intervals having weak specification is Devaney chaotic. Moreover, it is shown that if the system has strong specification then the result is true in general. Specification properties of induced systems on hyperspaces and probability measures spaces are also studied. Examples/counterexamples are provided wherever necessary to support results obtained.