Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (S1): 46-51.

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Chaos in the Semi-Flows and its Inverse Limit systems

He Lianfa, Zhang Zhenguo   

  1. 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

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

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