Related papers: On almost specification and average shadowing prop…

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,…

Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…

For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.

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 construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [Israel J. Math. 192 (2012), no. 2, 785--817]. Elaborating on our examples we…

We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…

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…

The following work presents a sufficiently general method for finding the parameters that characterise self-gravitating compact objects when their shadow contour is explicitly set. This method can be used in various algorithms to analyse…

Motivated by three recent open questions in the study of linear dynamics, we study weighted shifts on sequence spaces. First, we provide an example of a weighted shift on a locally convex space whose topology is generated by a sequence of…

We examine dynamical systems with the property that pseudo-orbits can be traced by small diameter sets with bounded cardinality. In particular, we show that mixing sofic subshifts and surjective dynamical systems with the specification…

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 define the concept of $(\mathscr{F},\mathscr{G})-$shadowing property on uniform space and say it as a topological $(\mathscr{F},\mathscr{G})-$shadowing property. We show that topological shadowing, topological…

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 point out a basic dichotomy between the shadowing and Lipschitz shadowing properties for one-sided shift spaces in two infinite-alphabet frameworks: the classical product-topology model $X\subseteq A^{\mathbb{N}}$ and the compact…

Families of regimes for discrete control systems are studied possessing a special quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the amplitudes of transient…

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few…

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…