Related papers: Periodic Shadowing for Set-Valued Maps
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…
In this paper, we study the dynamics of set-valued maps whose graphs are open and such that the image of each point is an open and connected set. Building upon the work of P. Duarte and M. Torres, who introduced and analyzed the…
In this note we study some properties of topological entropy for noncompact non-metrizable spaces.
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
For an $\alpha$-expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has…
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters…
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…
In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…
We study the metric mean dimension of $\Phi$-irregular set $I_{\Phi}(f)$ in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class $Y$, the values…
We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the $C^1$-interior of the set of all diffeomorphisms having so-called inverse periodic…
We define shadowable points for homeomorphism on metric spaces. In the compact case we will prove the following results: The set of shadowable points is invariant, possibly nonempty or noncompact. A homeomorphism has the pseudo-orbit…
We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…
In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…
The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…
We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset $A$, dense in the non-wandering set, where the barycenter property holds. To…