Related papers: Transitive points via Furstenberg family

Let $G = (V, E)$ be a graph where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say that $A$ \emph{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$. A…

Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage…

In his 1964 paper on f-expansions, Parry studied piecewise-continuous, piecewise-monotonic maps F of the interval [0,1), and introduced a notion of topological transitivity different from any of the modern definitions. This notion, which we…

Let $\mathcal X$ be an infinite locally compact separable metric space with metric $\rho$ and let $f : \mathcal X \longrightarrow \mathcal X$ be a continuous weakly mixing map. Let $\beta = \sup \big\{ \rho(x, y): \{x, y \} \subset \mathcal…

We consider topological dynamical systems $(X,T)$, where $X$ is a compact metrizable space and $T$ denotes an action of a countable amenable group $G$ on $X$ by homeomorphisms. For two such systems $(X,T)$ and $(Y,S)$ and a factor map $\pi…

If F is a type-definable family of commensurable subsets, subgroups or sub-vector spaces in a metric structure, then there is an invariant subset, subgroup or sub-vector space commensurable with F. This in particular applies to…

Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle number conserving systems where particle…

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

We obtain new bounds for (a variant of) the Furstenberg set problem for high dimensional flats over $\mathbb{R}^n$. In particular, let $F\subset \mathbb{R}^n$, $1\leq k \leq n-1$, $s\in (0,k]$, and $t\in (0,k(n-k)]$. We say that $F$ is a…

Let X be a coherent configuration associated with a transitive group G. In terms of the intersection numbers of X, a necessary condition for the point stabilizer of G to be a TI-subgroup, is established. Furthermore, under this condition, X…

We study for a dynamical system $f:X\longrightarrow X$ some of the principal topological recurrence-kind properties with respect to the induced maps $\overline{f}:\mathcal{K}(X)\longrightarrow\mathcal{K}(X)$, on the hyperspace of non-empty…

This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…

We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…

We view a design $\mathcal{D}$ as a set of $k$-subsets of a fixed set $X$ of $v$ points. A $k$-subset of $X$ is at distance $i$ from $\mathcal{D}$ if it intersects some $k$-set in $\mathcal{D}$ in $k-i$ points, and no subset in more than…

Systems obtained by quotienting a subshift of finite type (SFT) by another SFT are called finitely presented in the literature. Analogously, if a sofic shift is quotiented by a sofic equivalence relation, we call the resulting system…

Let ${\mathcal P}\subset{\mathbb Z}^2$ be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal P}$ is uniquely determined by the labeling of all other…

We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct…

We investigate quantum phase transitions in a topological Josephson junction with an embedded ferromagnetic layer, revealing a rich landscape of critical phenomena. The low-energy excitations comprise Majorana fermions propagating along the…

We discuss topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of 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…