Related papers: Shadowing With Small Diameter Sets Of Bounded Card…

We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…

Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices…

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a…

An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As…

In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and…

Cardinal characteristics of the continuum represent the boundaries in size between the countable and the continuum with respect to certain properties of sets. They are often defined as the minimum sizes of families of reals that meet some…

This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…

Given a compact metric space $X$ and an upper semicontinuous function $F\colon X \to 2^X$, we explore the dynamic system $(X,F)$. In this study, we introduce new concepts, demonstrate various results, and provide numerous examples. In…

We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…

In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system $(X,f)$ has shadowing, then it is…

We consider low-dimensional systems with the shadowing property. In dimension two, we show that the shadowing property for a homeomorphism implies the existence of periodic orbits in every $\epsilon$-transitive class, and in contrast we…

Let $(X,T)$ be a compact dynamical system. This article proves that if $(X,T)$ has the partial specification property, then it has the average shadowing property. It is also proven that if $(X,T)$ is surjective and has the partial…

We provide an explicit S-adic representation of rank one subshifts with bounded spacers and call the subshifts obtained in this way ''Ferenczi subshifts''. We aim to show that this approach is very convenient to study the dynamical behavior…

We investigate the approximate j-dimensionality of the singularity sets of minimal surfaces prescribed by Simon. This leads to the clasification of 8 variations of approximately j-dimensional surfacs in terms of dimension and locally finite…

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…

For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove…

Let $(X,G,\Phi)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property,…