Non-wandering sets of the powers of maps of a tree |
| |
Authors: | HUANG Wen YE Xiangdong HUANG Wen |
| |
Institution: | Department of Mathematics, University of Science and Technology of China, |
| |
Abstract: | Let T be a tree and let Ω ( f ) be the set of non-wandering points of a continuous map f: T→ T. We prove that for a continuous
map f: T→ T of a tree T: ( i) if x∈ Ω( f) has an infinite orbit, then x∈ Ω( fn) for each n∈ ℕ; (ii) if the topological entropy of f is zero, then Ω( f) = Ω( fn) for each n∈ ℕ. Furthermore, for each k∈ ℕ we characterize those natural numbers n with the property that Ω(fk) = Ω(fkn) for each continuous map f of T. |
| |
Keywords: | non-wandering point tree entropy |
本文献已被 万方数据 SpringerLink 等数据库收录! |