Zeta functions and topological entropy of periodic nonautonomous dynamical systems
type: Item
instance of: scholarly article
title: Zeta functions and topological entropy of periodic nonautonomous dynamical systems
zbMATH Open document ID: 1280.37024
author: João Ferreira Alves
author: Michal Málek
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-19T00:00:00Z
review text: Let \((f_1,f_2,\dots,f_k,\dots)\) be a \(k\)-periodic (\(k\) is a positive integer) sequence of piecewise monotone maps. The paper under review extends the Artin-Mazur zeta functions to the setting of periodic sequences of maps. Although some differences with the autonomous case (\(k=1\)) appear, it is proved that the zeta function does not need to be meromorphic. The authors find sufficient conditions to guarantee that the zeta function is meromorphic and the topological entropy can be computed using the periodic points of the sequence. The positive results are proved for sequences of maps such that the so-called crossing sets \(C_{i,j}=\{ x\in [0,1]:f_i(x)=f_j(x)\}\) for \(i,j=1,\dots,k\) are finite unions of compact intervals.
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37C30
zbMATH DE Number: 6155678
zbMATH Keywords: nonautonomous discrete systems
zbMATH Keywords: zeta functions
zbMATH Keywords: topological entropy
reviewed by: Jose S. Canovas
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.465
OpenAlex ID: W2325917823
DOI: 10.3934/DCDS.2013.33.465
description: scientific article; zbMATH DE number 6155678