摘要
设f∈C°(T,T)是树T上的连续自映射,N为自然数集,则下述条件等价: 1)f有异状点; 2)f的拓扑熵大于零; 3)存在m∈N使得{mk:k∈N}(?)Per(f); 4)存在n∈N使得fn具有2-马蹄。
Let f be a continuous map of a tree T into itself. It is shown that the following statements are equivalent：
1） f has a homoclinic point;
2） f has positive topological entropy;
3） There exists an m E N such that {mk ： k ∈ N} 包含 Per（f）;
4） There exists an n E N such that f^n has a 2-horseshoe.
出处
《工程数学学报》
CSCD
北大核心
2006年第2期350-354,共5页
Chinese Journal of Engineering Mathematics
基金
Scientific Research Fund of Hunan Provincial Education Department of China(02C188) Postdoctor Scientific Fundation of Central South University
关键词
树映射
分支点
异状点
马蹄
tree map
branching point
homoclinic point
horseshoe
