CHAIN RECURRENT POINTS AND TOPOLOGICAL ENTROPY OF A TREE MAP  

作　　者：Sun TaixiangDept.of Math.,Guangxi Univ.,Nanning 530004 Dept. of Math.,Univ. of Science and Technology of China,Hefei 230026,China. 

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2002年第3期313-318,共6页高校应用数学学报（英文版）（B辑）

基　　金：the National Natural Science Foundation of China(1 996 1 0 0 1 ) and SF of Guangxi(0 1 3 5 0 2 7)

摘　　要：Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.

关 键 词：tree map DIVISION chain recurrent point topological entropy the set of chain equivalent points. 

分 类 号：O189.1[理学—数学]