摘要
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∈ ?; (ii) if the topological entropy of f is zero, then Ω( f) = Ω( fn) for each n∈ ?. Furthermore, for each k∈ ? we characterize those natural numbers n with the property that Ω(fk) = Ω(fkn) for each continuous map f of T.
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.
基金
This work was supported by the National Natural Science Foundation of China (Grant No. 19625103) .
