Related papers: The interplay between partial specification, avera…

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…

We prove that if a topological dynamical system $(X,T)$ is surjective and has the vague specification property, then its ergodic measures are dense in the space of all invariant measures. The vague specification property generalises Bowen's…

It is proved that to every invariant measure of a compact dynamical system one can associate a certain asymptotic pseudo orbit such that any point asymptotically tracing in average that pseudo orbit is generic for the measure. It follows…

We show that the vague specification property is strictly weaker than most of the specification-like properties, by establishing its equivalence with the asymptotic average shadowing property. In particular, we see that the weak…

We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing…

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…

In this paper we present a systematic study of shadowing properties with average error in tracing such as (asymptotic) average shadowing, $\underline{d}$-shadowing, $\overline{d}$-shadowing and almost specification. As the main tools we…

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…

We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points…

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…

In this paper, we explore a topological system $f:M\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\subseteq\mathcal {M}_{inv}(f)$ coincides with…

For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost 1-1 extensions. For a topologically transitive system with the…

The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a…

In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…

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,…

We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative…

In the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff…

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 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of shadowing, average shadowing, transitive,…

Let $\left(X_n, d_n\right)$ be a sequence of metric spaces and let $\mathcal{F}=\left\{f_n\right\}_{n \in \mathbb{Z}}$ be a sequence of continuous and onto maps $f_n: X_n \rightarrow X_{n+1}, n \in \mathbb{Z}_{+}$. In this paper, we prove…