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

作者：Huang W^*; Ye XD

来源：Science in China Series A-Mathematics, 2001, 44(1): 31-39.

DOI：10.1007/BF02872280

• non-wandering point
• tree
• entropy

Let T be a tree and let Omega (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 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 topological 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 those natural numbers n with the property that Omega (f(k)) = Omega (f(kn)) for each continuous map f of T.

• 出版日期2001-1
• 单位中国科学技术大学