Non-wandering sets of the powers of maps of a tree

Authors
Citation
W. Huang et Xd. Ye, Non-wandering sets of the powers of maps of a tree, SCI CHINA A, 44(1), 2001, pp. 31-39
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN journal
1001-6511 → ACNP
Volume
44
Issue
1
Year of publication
2001
Pages
31 - 39
Database
ISI
SICI code
1001-6511(200101)44:1<31:NSOTPO>2.0.ZU;2-3
Abstract
Let T be a tree and let Omega (f) be the set of non-wandering points of a c ontinuous map f: T-->T. We prove that for a continuous map f: T-->T of a tr ee T: (i) if x is an element of Omega( f) has an infinite orbit, then x is an element of Omega (f(n)) for each n is an element ofN; (ii) if the topolo gical entropy of f is zero, then Omega (f) = Omega (f(n)) for each n is an element ofN. Furthermore, for each k is an element ofN we characterize thos e natural numbers n with the property that Omega (f(k)) = Omega (f(kn)) for each continuous map f of T.