Graph maps whose periodic points form a closed set

作者：Mai Jie Hua; Shao Song^*

来源：Journal of Mathematical Analysis and Applications, 2010, 371(2): 649-654.

DOI：10.1016/j.jmaa.2010.05.062

• Graph map
• Periodic point
• omega-limit point
• Recurrent point

A continuous map f from a graph G to itself is called a giaph map. Denote by P(f), R(f), omega(f), Omega(f) and CR(f) the sets of periodic points, recurrent points, omega-limit points, non-wandering points and chain recurrent points of f respectively. It is well known that P(f) subset of R(f) subset of w(f) subset of Omega(f) subset of CR(f). Block and Franke (1983) [5] Proved that if f . 1 -> I is an interval map and P(f) is a closed set, then CR(f) = P(f). In this paper we show that if f . G -> G is a graph map and P(f) is a closed set, then omega(f) = R(f). We also give an example to

• 出版日期2010-11-15
• 单位汕头大学; 中国科学技术大学