半流及其逆极限的混沌

Chaos in the Semi-Flows and its Inverse Limit systems

该文对连续动力系统研究了Devaney意义下的混沌的不变性质．证明了：（1）半流是混沌的（resP，ω混沌的）当且仅当它的逆极限是混沌的（resp,ω混沌的）；（2）自映射是混沌的（resp.ω混沌的）当且仅当它的扭扩半流是混沌的（resp．ω混沌的）；（3）自映射逆极限的扭扩流拓扑共轭于其扭扩半流的逆极限．从（2）和（3）可知，结论（1）是对自映射的推广．

in this paper,we study the invariants of the chaos in the sense of Devaney for continuous dynamical systems. The followings is proved: (1 ) a semi-flow is chaotic (resp. ω- chaotic) iff inverse limit system of it is chaotic (resp. ω-chaotic); (2) a continuous mcap is chaotic (resp. ω-chaotic) iff suspension semi-flow of it is chaotic (resp. ω-chaotic); (3) suspension flow of inverse limit system of a continuous map is conjugate to inverse limit system of suspension semi-flow of it. It follows from (2) and (3)that (1) is a generalizafion of those obtained for discrete dynamical systems in [4].