Related papers: Shadowing, recurrence, and rigidity in dynamical s…
For continuous maps of compact metric spaces $f:X\to X$ and $g:Y\to Y$ and for various notions of topological recurrence, we study the relationship between recurrence for $f$ and $g$ and recurrence for the product map $f\times g:X\times Y…
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…
We show that a doubly minimal system $X$ has the property that for every minimal system $Y$ the orbit closure of any pair $(y,x) \in Y \times X$ is either $Y \times X$ or it has the form $\Gamma_\pi = \{(\pi(x),x) : x \in X\}$ for some…
The stability theory of compact metric spaces with positive topological dimension is a well-established area in Dynamical Systems. A central result, attributed to Walters, connects the concepts of topological stability and the shadowing…
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
A {\it dynamical system\/} is a pair $(X,\langle T_s\rangle_{s\in S})$, where $X$ is a compact Hausdorff space, $S$ is a semigroup, for each $s\in S$, $T_s$ is a continuous function from $X$ to $X$, and for all $s,t\in S$, $T_s\circ…
A set $A \subseteq \mathbb{N}$ is a set of pointwise recurrence if for all minimal dynamical systems $(X, T)$, all $x \in X$, and all open neighborhoods $U \subseteq X$ of $x$, there exists a time $n \in A$ such that $T^n x \in U$. The set…
We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic…
In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism…
Let X_1 and X_2 be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map X_1 to X_2 is affine (that is, X_2 is topologically rigid) if and only if the system X_2 has…
Poincar\'e recurrence theorem implies the density of recurrent points for volume-preserving dynamical systems on compact domains. The density of closed orbits in the non-wandering set is one of the essential properties of Axiom A and chaos.…
This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…
In this paper, we study continuum-wise expansive non-autonomous discrete dynamical systems. We discuss various properties of such non-autonomous systems. We further obtain results for cw-expansive non-autonomous systems with shadowing…
We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…
Let $A\subset \mathbb{N}$. We say $A$ is an $R$-sequence for a given minimal system $(Y,S)$ if there is $y\in Y$ such that $\{S^ny:n\in A\}$ is dense in $Y$. Richter asked if $A$ is an $R$-sequence for all minimal equicontinuous systems…
We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full shifts are expansive. We show that every expansive continuous…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.
In this work we focus on the phase space singularities of interactive quintessence model in the presence of matter fluid. This model is related to swampland studies, that the outcomes affect all these Swampland related models with the same…
Let $\phi$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_{\phi}f=f\circ \phi$ on the Hardy space $H^2(\mathbb{D}).$ We mainly characterize all…