Specification and Thermodynamic Properties of Topological Time-Dependent Dynamical Systems

Sarkooh, Javad Nazarian; Ghane, F.H.

doi:10.48550/arxiv.1712.06109

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“…They have related specification property to topological mixing, shadowing and distality in non-autonomous systems. In 2017, authors have proved that any non-autonomous system having the weak specification property has positive topological entropy and that each uniformly expanding non-autonomous system satisfies the shadowing and the specification properties [17]. Recently, in 2018, authors have studied stronger forms of sensitivity for non-autonomous discrete dynamical systems [15,23].…”

Section: Introductionmentioning

confidence: 99%

Specification properties for non-autonomous discrete systems

Salman,

Das

2018

Preprint

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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 whereas 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/counter examples are provided wherever necessary to support results obtained.

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Section: Introductionmentioning

confidence: 99%