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The ω-limit sets of a flow and periodic orbits

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  • Wang, Xiaoxia
  • Blackmore, Denis
  • Wang, Chengwen

Abstract

In this paper we discuss the ω-limit sets of a flow using the Conley theory, chain recurrence and Morse decompositions. Our results generalize and improve the related result in [Schropp J. A reduction principle for ω-limit sets. Z Angew Math Meth 1996;76(6):349–56], and we also show how they can be used as a basis for some new criteria for the existence of periodic orbits.

Suggested Citation

  • Wang, Xiaoxia & Blackmore, Denis & Wang, Chengwen, 2009. "The ω-limit sets of a flow and periodic orbits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2690-2696.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2690-2696
    DOI: 10.1016/j.chaos.2008.10.004
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