The -limit sets of a flow and periodic orbits |
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| Authors: | Xiaoxia Wang Denis Blackmore Chengwen Wang |
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| Institution: | aSchool of Science, Beijing Jiaotong University, Beijing 100044, China;bDepartment of Mathematical Sciences and CAMS, New Jersey Institute of Technology, Newark, NJ 07102, USA;cDepartment of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA;dDepartment of Mathematics, Essex County College, Newark, NJ 07102, USA |
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| 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. |
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