Related papers: Exploring stronger forms of transitivity on G-spac…
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.
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…
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…
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, the notions of transitivity and homogeneity in binary $G$-spaces are studied. These notions coincide for distributive binary $G$-spaces. For compact $G$, it is shown that distributive transitive binary $G$-spaces are coset…
In this paper, we investigate the dynamical behavior of a two dimensional shift $X_G$ (generated by a two dimensional graph $G=(\mathcal{H},\mathcal{V})$) using the adjacency matrices of the generating graph $G$. In particular, we…
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…
Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…
We improve previous results by exhibiting a construction that contains all known examples. A suficient condition for the existence of robustly transitive maps displaying singularities on a certain large class of compact manifolds is given.
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).…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
We investigate algebraic and topological transitivity and, more generally, k-transitivity for linear spaces of operators. In finite dimensions, we determine minimal dimensions of k-transitive spaces for every k, and find relations between…
We will consider here some dynamics of the tangent map, weaker than hyperbolicity, and we will discuss if these structures are rich enough to provide a good description of the dynamics from a topological and geometrical point of view. This…
Motivated by the notion of strong computable type for sets in computable analysis, we define the notion of strong computable type for $G$-shifts, where $G$ is a finitely generated group with decidable word problem. A $G$-shift has strong…
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…
In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…
Maps $f,g\colon I\to I$ are called strongly commuting if $f\circ g^{-1}=g^{-1}\circ f$. We show that strongly commuting, piecewise monotone maps $f,g$ can be decomposed into a finite number of invariant intervals (or period 2 intervals) on…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.
We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…