【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。更多还原

【Abstract】 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∈N such that {mk : k ∈ N} (?) Per(f); 4) There exists an n ∈ N such that fn has a 2-horseshoe.更多还原