Sets of periods of dynamical systems
type: Item
instance of: scholarly article
title: Sets of periods of dynamical systems
zbMATH Open document ID: 1196.37071
author: V. Kannan
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2010-07-09T00:00:00Z
review text: From the Introduction: Dynamics is the study of eventual behaviour of orbits. The periodic orbits are the simplest kind of orbits. Therefore it is natural to investigate answers to the following general scheme of question: In a dynamical system \((X,f)\), what are all the lenths of the cycles there? In this article, we present a coherent, though not exhausitive, account of some well-known and some rexent results of many mathematicians (including our own) on the following question: Given a `nice' class of dynamical systems, which subsets of \(\mathbb{N}\) arise as the sets of periods of members of that class? While stating and explaining some elegant answers, proofs have been outlined or indicated occasionally.
reviewed by: Feng Xie
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37E15
Mathematics Subject Classification ID: 37E25
Mathematics Subject Classification ID: 37B15
zbMATH DE Number: 5734658
zbMATH Keywords: Sets of periods
zbMATH Keywords: Sarkovskii's theorem
zbMATH Keywords: Baker's theorem
zbMATH Keywords: trees
zbMATH Keywords: transive maps
zbMATH Keywords: toral automorphisms
zbMATH Keywords: cellular automata
zbMATH Keywords: subshift of finite type
zbMATH Keywords: linear operator
MaRDI profile type: Publication
full work available at URL: s13226-010-0008-y
OpenAlex ID: W2144719318
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DOI: 10.1007/S13226-010-0008-Y
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description: scientific article; zbMATH DE number 5734658