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The isolated invariant sets of a flow
- Source :
- Chaos, Solitons & Fractals. 12:453-461
- Publication Year :
- 2001
- Publisher :
- Elsevier BV, 2001.
-
Abstract
- Some definitions such as m-chain recurrent set, weakly gradient flow and generalized Morse decomposition for a flow defined on a topological space are introduced in this paper. Some conclusions, include the chain recurrent set contain the m-chain recurrent set; the m-chain recurrent set contain the non-wandering set, are proved. In some flows the non-wandering set is proper subset of the m-chain recurrent set; in the meantime the m-chain recurrent set is proper subset of the chain recurrent set. Moreover some criterions for the existence of trajectories joining singular points and a necessary and sufficient condition of the weakly gradient flow are also given here. At last the generalized Morse decomposition of the invariant set are discussed in the paper.
Details
- ISSN :
- 09600779
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........9b60263c42c4faf017221e328e76512d