Entropies and spectra
type: Item
instance of: scholarly article
title: Entropies and spectra
zbMATH Open document ID: 0841.58039
author: Laurent Guillopé
published in: Osaka Journal of Mathematics
publication date: 1995-02-09T00:00:00Z
review text: This is a broad survey of various results concerning the asymptotic growth of ``certain quantities'' related to entropy of a given dynamical system. For example, when the dynamical system is defined by an integer (or real) action, the asymptotic growth rate of the number of periodic points (or periodic orbits) of (primitive) period \(p\) is related to the entropy if the underlying dynamics is ``hyperbolic''. For dynamical systems defined by the actions of discrete subgroups of isometries of the hyperbolic space, asymptotics of the growth rates of several analogous quantities have been studied. Yet another situation where similar notions and results can be developed is the example of group actions on graphs and trees. This paper describes various known results and it gives exact expressions for asymptotics of growth rates of various relevant quantities in all these situations.
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 720165
zbMATH Keywords: asymptotic growth
zbMATH Keywords: entropy
zbMATH Keywords: dynamical system
zbMATH Keywords: periodic points
zbMATH Keywords: asymptotics
reviewed by: Mahesh Nerurkar
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 720165