Related papers: Topological entropy, mean dimension, and weakly eq…

For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…

Let $\boldsymbol{X}=\{X_{k}\}_{k=0}^{\infty}$ be a sequence of compact metric spaces $X_{k}$ and $\boldsymbol{T}=\{T_{k}\}_{k=0}^{\infty}$ a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$. The pair…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…

Using the idea of local entropy theory, we characterize the sequence entropy tuple via mean forms of the sensitive tuple in both topological and measure-theoretical senses. For the measure-theoretical sense, we show that for an ergodic…

Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and correspond to (non-linear in general) functionals that are linear on singly…

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…

Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various…

In this paper, we study the regularity of topological entropy, as a function on the space of Riemannian metrics endowed with the $C^0$ topology. We establish several instances of entropy robustness (persistence of entropy non-vanishing…

In this paper, we consider two questions about topological entropy of dynamical systems. We propose to resolve these questions by the same approach of using \'etale analogs of topological and algebraic dynamical systems. The first question…

In this paper, we are concerned with the shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water…

We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their…

This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…

In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…

In this work, we study pmp actions of countable groups on arbitrary diffuse probability spaces under the point of view of weak equivalence. We will show that any such an action is weakly equivalent to an action on a standard probability…

We consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a Riemannian metric $g$ of negative curvature with fixed total area. The second author has shown that the topological entropy of geodesic flow for $g$ is greater than…

The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the…

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic…