Work

Discretization strategies for computing Conley indices and Morse decompositions of flows

Year: 2016

Type: article

Abstract: Conley indices and Morse decompositions of flows can be found by using algorithms whichrigorously analyze discrete dynamical systems. This usually involves integrating a timediscretization of the flow using interval arithmetic.We compare the old idea of fixing a time step as a parameter toa time step continuously varying in phase space.We present an example where this second strategy necessarily yields betternumerical outputs and prove that our outputs yield a valid Morsedecomposition of the given flow.

Source: Journal of Computational Dynamics

DOI: 10.3934/jcd.2016001

Authors: Konstantin Mischaikow, Marian Mrozek, Frank Weilandt

Institution: Jagiellonian University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond