# American Institute of Mathematical Sciences

January  2016, 3(1): 1-16. doi: 10.3934/jcd.2016001

## Discretization strategies for computing Conley indices and Morse decompositions of flows

 1 Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854-8019, United States 2 Division of Computational Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland, Poland

Received  April 2015 Revised  July 2016 Published  August 2016

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.
Citation: Konstantin Mischaikow, Marian Mrozek, Frank Weilandt. Discretization strategies for computing Conley indices and Morse decompositions of flows. Journal of Computational Dynamics, 2016, 3 (1) : 1-16. doi: 10.3934/jcd.2016001
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