Conley's fundamental theorem of dynamical systems
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Conley's fundamental theorem of dynamical systems or Conley's decomposition theorem states that every flow of a dynamical system with compact phase portrait admits a decomposition into a chain-recurrent part and a gradient-like flow part.[1] Due to the concise yet complete description of many dynamical systems, Conley's theorem is also known as the fundamental theorem of dynamical systems.[2][3] Conley's fundamental theorem has been extended to systems with non-compact phase portraits[4] and also to hybrid dynamical systems.[5]
