Related papers: Shadowing and mixing on systems of countable group…

We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…

We investigate the role of the global driving phase $\Phi$ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with…

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 discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we…

We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…

In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show…

Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…

We consider perturbed discrete tight-binding models in $\ell^2(\mathbb{Z_h},\mathcal{G})$ describing union of quantum particles with localized interactions, where $\mathbb{Z_h}$ is the 1D lattice $h\mathbb{Z_h}$, $h > 0$, and $\mathcal G$…

We introduce the strong Gelfand-Phillips property for locally convex spaces and give several characterizations of this property. We characterize the strong Gelfand-Phillips property among locally convex spaces admitting a stronger Banach…

Let $G$ be a group acting via ring automorphisms on an integral domain $R.$ A ring-theoretic property of $R$ is said to be $G$-invariant, if $R^G$ also has the property, where $R^G=\{r\in R \ | \ \sigma(r)=r \ \text{for all} \ \sigma\in…

Let ${\mathcal A}\subset {\mathcal P}(X)$, $\emptyset, X\in {\mathcal A}$, ${\mathcal A}$ being closed under finite intersections. If $\psi={o},\omega,\gamma$, then $\Psi({\mathcal A})$ is the family of those $\psi$-covers ${\mathcal U}$…

Let $G$ be a finite group and $H$ be a subgroup of $G$. Then $H$ is called a weakly $S\Phi$-supplemented subgroup of $G$, if there exists a subgroup $T$ of $G$ such that $G =HT$ and $H \cap T \leq \Phi (H) H_{sG}$, where $H_{sG}$ denotes…

We introduce and analyze a Spencer-type elliptic complex on the space of differential forms valued in symmetric powers of an adjoint bundle, $\Omega^\bullet(X)\otimes \mathrm{Sym}^\bullet(G)$. The complex is governed by a total differential…

Let G be a finite group. We explore the model theoretic properties of the class of differential fields of characteristic zero in m commuting derivations equipped with a G-action by differential field automorphisms. In the language of…

In the study manifolds of Ricci curvature bounded below, a stumbling obstruction is the lack of links between large-scale geometry and small-scale geometry at a fixed reference point. There have been few links (volume, dimension) when the…

Let X be a topological Hausdorff space together with a continuous action of a finite group G. Let R be the ring of integers of a number field F. Let E be a G-sheaf of flat R-modules over X and let $\Phi$ be a G-stable paracompactifying…

A continuous action of a group G on a compact metric space has sensitive dependence on initial conditions if there is a number e>0 such that for any open set U we can find g in G such that g.U has diameter greater than e. We prove that if a…

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. Let $X$ be a product of…

We prove that: 1. If a Hausdorff M-space is a continuous closed image of a submetrizable space, then it is metrizable. 2. A dense-in-itself open-closed image of a submetrizable space is submetrizable if and only if it is functionally…

Let $G$ be an infinite countable amenable group and let $(X,G)$ be a $G$-subshift with specification, containing a free element. We prove that $(X,G)$ is universal, i.e., has positive topological entropy and for any free ergodic $G$-action…