Related papers: Entropy via multiplicity

This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an…

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…

This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…

Let $M$ be a closed surface and $f$ a diffeomorphism of $M$. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we…

We establish the analogue for maps on trees of the result established in two papers by the first author for interval maps, that a continuous self- map for which all but countably many points have at least m preimages (and none have less…

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…

In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…

Let $G$ be a topological group, let $\phi$ be a continuous endomorphism of $G$ and let $H$ be a closed $\phi$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is,…

In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…

Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…

This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…

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…

A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…

We investigate mixing properties of piecewise affine non-Markovian maps acting on $[0,1]^2$ or $[0,1]^3$ and preserving the Lebesgue measure, which are natural generalizations of the {\it heterochaos baker maps} introduced in [Y. Saiki, H.…

The purpose of this work is to bound sofic topological entropy of Toeplitz systems over residually finite groups and to prove the Krieger Theorem about attaining arbitrary entropy by the Toeplitz systems. To achieve these results, we…

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…

In this paper, we introduce topological entropy for dynamical systems generated by a single local homeomorphism (Deaconu-Renault systems). More precisely, we generalize Adler, Konheim, and McAndrew's definition of entropy via covers and…

We study the complexity of the itineraries of injective piecewise contracting maps on the interval. We prove that for any such map the complexity function of any itinerary is eventually affine. We also prove that the growth rate of the…

We show that for a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) on a non-empty compact metrizable space $\Omega$, the existence of a affine space dense in the set of continuous functions on $\Omega$ constituted by elements…