Related papers: On notions of determinism in topological dynamics

In this article we extend the notion of expansivity from topological dynamics to automorphisms of commutative rings with identity. We show that a ring admits a 0-expansive automorphism if and only if it is a finite product of local rings.…

Here we define and study the properties of retrodictive inference. We derive equations relating retrodiction entropy and thermodynamic entropy, and as a special case, show that under equilibrium conditions, the two are identical. We…

Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using…

The purpose of this paper is to generalize the variational principle, which states that the topological entropy is equal to the supremum of the measure theoretical entropies and also the minimum of the metric theoretical entropies, to…

Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different…

For a measurable map $T$ and a sequence of $T$-invariant probability measures $\mu_n$ that converges in some sense to a $T$-invariant probability measure $\mu$, an estimate from below for the Kolmogorov--Sinai entropy of $T$ with respect to…

In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dynamical system, we define measure-theoretical restricted…

For $C^{1+}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbolic measure of maximal entropy. We then apply this to study…

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for…

We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically…

We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.

A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…

Present theoretical predictions for the entanglement entropy through topological defects are violated by numerical simulations. In order to resolve this, we introduce a paradigm shift in the preparation of reduced density matrices in the…

Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…

A recent result of Downarowicz and Serafin (DS) shows that there exist positive entropy subshifts satisfying the assertion of Sarnak's conjecture. More precisely, it is proved that if $y=(y_n)_{n\ge 1}$ is a bounded sequence with zero…

We generalize the definition of topological entropy given by Adler, Konheim, and McAndrew (AKM) for piecewise continuous self-maps defined on a compact interval (pc-maps). For this notion of entropy, we prove that the properties of the…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…