Related papers: Strong topological transitivity, hypermixing, and …
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…
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.
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…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
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 show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
In this paper we introduce and study some stronger forms of transitivity like total transitivity, weakly mixing for maps on G-spaces. We obtain their relationship with the earlier defined notion of strongly mixing for maps on G-spaces. We…
Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mixing properties between…
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…
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…
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…
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous…
We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling…
For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
Motivated by three recent open questions in the study of linear dynamics, we study weighted shifts on sequence spaces. First, we provide an example of a weighted shift on a locally convex space whose topology is generated by a sequence of…
In this paper, we introduce and study the notions of $\Delta$-mixing, $\Delta$-transitivity, mildly mixing, strong multi-transitivity and multi-transitivity with respect to a vector in non-autonomous discrete dynamical systems (NDS).…
We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…