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On Conley’s fundamental theorem of dynamical systems. (English) Zbl 1068.37008

Summary: We generalize Conley’s fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of a regular index filtration for every Morse decomposition.

MSC:

37B30 Index theory for dynamical systems, Morse-Conley indices
37B25 Stability of topological dynamical systems
37B35 Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
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