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.