Discretization strategies for computing Conley indices and Morse decompositions of flows
Konstantin Mischaikow Marian Mrozek Frank Weilandt
Conley indices and Morse decompositions of flows can be found by using algorithms which rigorously analyze discrete dynamical systems. This usually involves integrating a time discretization of the flow using interval arithmetic. We compare the old idea of fixing a time step as a parameter to a time step continuously varying in phase space. We present an example where this second strategy necessarily yields better numerical outputs and prove that our outputs yield a valid Morse decomposition of the given flow.
keywords: Morse decomposition rigorous numerical algorithm. Conley index interval arithmetic

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