Related papers: Mixing properties in coded systems
We show that a coded system is mixing if and only if it is totally transitive and if in addition it has a relatively prime generator, then it has strong property P. We continue by showing that a mixing half-synchronized system has such a…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…
The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…
In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…
We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.
Given a switched system, we introduce weakly mixing sets of type 1, 2 and Xiong chaotic sets of type 1, 2 with respect to a given set and show that they are equivalent respectively.
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the…
This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologically mildly mixing, then it is mild mixing of higher orders…
It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is…
We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing…
We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift $X$ and its associated hom tree-shift $\mathcal{T}_{X}$, as well as the equivalence in the sofic shift. On the…