Non-wandering points and the depth of a graph map

Authors
Citation
Xd. Ye, Non-wandering points and the depth of a graph map, J AUS MAT A, 69, 2000, pp. 143-152
Citations number
13
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
0263-6115 → ACNP
Volume
69
Year of publication
2000
Part
2
Pages
143 - 152
Database
ISI
SICI code
0263-6115(200010)69:<143:NPATDO>2.0.ZU;2-C
Abstract
Let f : G --> G be a continuous map of a graph and let d(A) denote the deri ved set (or limit points) of A subset of G. We prove that d(Omega>(*) over bar * (f)) subset of Lambda>(*) over bar * (f) and the depth of f is at mos t three. We also prove that if f is piecewise monotone or has zero topologi cal entropy, then the depth of f is at most two. Furthermore, we obtain som e results on the topological structure of Omega>(*) over bar * (f). 2000 Ma thematics subject classification: primary 54H20, 58F03.