Related papers: On specification and measure expansiveness

We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our…

For any continuous self-map of a compact metric space, we consider the space of chain components and prove that the s-limit shadowing implies the denseness of chain components with the shadowing property. It gives a partial answer to a…

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,…

This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…

We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…

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 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…

Since seminal work of Bowen, it has been known that the specification property implies various useful properties about a topological dynamical system, among them uniqueness of the measure of maximal entropy (often referred to as intrinsic…

This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various…

We investigate local entropy theory, particularly the property of having completely positive entropy (CPE), from a descriptive set-theoretic point of view. We aim to determine descriptive complexity of different families of dynamical…

In this paper, we further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expansion in the links imply the global expansion phenomena of…

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…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

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…

This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…

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…

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…

We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to…

This paper aims at formulating definitions of topological stability, structural stability, and expansiveness property for an iterated function system( abbrev, IFS). It is going to show that the shadowing property is necessary condition for…

In this paper, we define bi-asymptotically $c$-expansive maps on metric spaces and study its relationship with other variants of expansivity such as bi-asymptotically expansive maps and $N$-expansive maps. We also provide an example to…