敏感依赖极小系统的复杂性

Complexity of sensitive dependence minimal dynamical systems

引进了一类新系统,即敏感依赖极小系统。一个紧致系统称为是敏感依赖极小的是指若该系统中存在子系统是敏感依赖的,则该子系统就是原系统。对于敏感依赖极小系统(X,f),如果BD+(f)-A(f)≠,本文得到f是拓扑传递的,f有满侧度中心的,f是Takens-Ruelle混沌。最后,还证明了敏感依赖极小性质是在拓扑共轭映射保持不变的性质。

As the sensitive dependence minimal system, a new kind of system was firstly introduced in this pa- per. A compact system was called to be sensitive dependence minimal if there was a subsystem. This subsystem was in accord with the original system. For the sensitive dependence minimal system （X,f） with BD＋（f）-A（f）≠φ,f was topologically transitive ,f has a full measure center and f is chaotic in the sense of Takens-Ruelle. It was shown that the sensitive dependence minimal property was invariant under the topologically conjugate mapping.