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arXiv · 1511.04426

Discretization strategies for computing Conley indices and Morse decompositions of flows

Konstantin Mischaikow·Marian Mrozek·Frank Weilandt
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Abstract

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 parameters 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.

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Konstantin Mischaikow, Marian Mrozek, Frank Weilandt. 2015-11-13. Discretization strategies for computing Conley indices and Morse decompositions of flows. https://arxiv.org/abs/1511.04426

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