In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

Finite type subshifts with finite number of symbols are important sort of discrete dynamical systems (often called symbolic dynamics) and are intensively studied [2, 3, 4, 5, 6]. Mañé proved a theorem (for finite type subshifts generated by 0, 1-square matrices), stating that topological transitivity and topological mixing can be reduced to algebraic properties of associated matrices [5]. In th...

Topological dynamical systems (X, T) are actions $$T\,{ \times }\, X \rightarrow X$$ , given as $$(t, x) \mapsto tx$$ on a compact Hausdorff topological space with T an acting group or monoid. We consider the property of transitivity especially for semiflows S) and discuss variations in its definitions. emphasize those properties that differ compared to flows (semi)cascades.

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

A quasi-continuous dynamical system is a pair ( X , f ) consisting of topological space and mapping : ? such that n for all ? N where the set non-negative integers. In this paper, we show under appropriate assumptions, various definitions concept transitivity are equivalent in system. Our main results establish equivalence point These extend some classical on continuous systems [3] [10] [24] [7...