半流及其逆极限的混沌

数学物理学报 ›› 1997, Vol. 17 ›› Issue (S1): 46-51.

半流及其逆极限的混沌

何连法, 张振国

河北师范大学数学系石家庄 050016

收稿日期:1995-10-11 修回日期:1996-07-01 出版日期:1997-12-26 发布日期:1997-12-26
基金资助:
国家自然科学基金

Chaos in the Semi-Flows and its Inverse Limit systems

He Lianfa, Zhang Zhenguo

Department of mathematics, Hebei Teachers' University, Shijiazhuang 050016, China

Received:1995-10-11 Revised:1996-07-01 Online:1997-12-26 Published:1997-12-26

摘要/Abstract

摘要： 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.

关键词: 半流, 逆极限, Devaney意义下的混沌, ω混沌, 扭扩半流

Abstract: 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].

Key words: Semi-flows, inverse limit systems, chaos, ω-chaos, suspenion semi-flows

何连法, 张振国. 半流及其逆极限的混沌[J]. 数学物理学报, 1997, 17(S1): 46-51.

He Lianfa, Zhang Zhenguo. Chaos in the Semi-Flows and its Inverse Limit systems[J]. Acta mathematica scientia,Series A, 1997, 17(S1): 46-51.