Related papers: Shadowing, sensitivity and entropy points

In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space.…

We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…

We define the concept of symmetric sensitivity with respect to initial conditions for the endomorphisms on Lebesgue metric spaces. The idea is that the orbits of almost every pair of nearby initial points (for the product of the invariant…

In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…

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…

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…

The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…

We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short…

This article is devoted to study which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive.…

In this note we study some properties of topological entropy for noncompact non-metrizable spaces.

We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for…

We study the possibility that black hole entropy be identified as entropy of entanglement across the horizon of the vacuum of a quantum field in the presence of the black hole. We argue that a recent proposal for computing entanglement…

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)…

The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…

Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…