【摘要】 设E为满足强分离条件的迭代函数系统的(X,f1,…,fN)吸引子,定义连续映射f:E→E,f(x)=fj-1(x),xfj(E),j=1,…,N.设(p1,p2,…,pN)为一个概率向量,μ为对应的不变测度.文中研究了上述映射的复杂动力学行为,得到如下结果:(1)对映射f,存在一个有限混沌集CE,满足μ(C)=μ(E)=1;(2)映射f存在Li-Yorke意义下混沌的极小子系统,该子系统具有零拓扑熵文中还对一些已知的结果进行了推广.更多还原

【Abstract】 In this paper,by supposing E to be the attractor of an iterated function system(X,f1,…,fN) which satisfies the strong separation condition,defining a continuous mapping f∶E→E,f(x)=f-1j(x),xfj(E),j=1,…,N,and setting(p1,p2,…,pN) as a probability vector and μ the corresponding invariant measure,some complex dynamical behaviors of the continuous mapping are investigated.The results indicate that,for the mapping f,there exists a finitely chaotic set CE satisfying μ(C)=μ(E)=1,and that the mapping f has some chaotic minimal subsystem with zero topological entropy in the sense of Li-Yorke.Some existing results are finally generalized in the paper.更多还原