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The \(\omega \)-limit sets of a flow and periodic orbits. (English) Zbl 1198.37034

Summary: We discuss the \(\omega \)-limit sets of a flow using the Conley theory, chain recurrence and Morse decompositions. Our results generalize and improve the related result of J. Schropp [Z. Angew. Math. Mech. 76, No. 6, 349–356 (1996; Zbl 0879.34049)], and we also show how they can be used as a basis for some new criteria for the existence of periodic orbits.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37B35 Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
34C25 Periodic solutions to ordinary differential equations
37B25 Stability of topological dynamical systems
37B30 Index theory for dynamical systems, Morse-Conley indices
37C27 Periodic orbits of vector fields and flows

Citations:

Zbl 0879.34049
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References:

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