设E为满足强分离条件的迭代函数系统的(Xf1…fN)吸引子,定义连续映射f:E→Ef(x)=f^-(x)x∈fj(E),…,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)对映射厂,存在一个有限混沌集CCE,满足μ(C)=μ(E)=1;(2)映射/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.
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→Ef(x) =f^-1j (x), x x∈fj(E), j = 1,..., N, and setting (p1 ,P2,…,PN) as a probability vector andμ the corresponding invariant measure, some complex dynamical behaviors of the continuous mapping are investigated. The results indicate that, for the mappingf, there exists a finitely chaotic set C CE satisfyingμ(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 tinally generalized in the paper.