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A topological approach to the algorithmic computation of the Conley index for Poincaré maps. (English) Zbl 1325.65175

Summary: A new algorithm for computing the Conley index of the Poincaré map of a time-periodic nonautonomous ordinary differential equation is presented. The algorithm is based on a theorem which reduces the computation of the index to the study of certain singular chains on an index pair for some small-step translation operator of the equation. In particular, no numerical enclosures of the Poincaré map are required. Concrete numerical examples for planar systems are provided.

MSC:

65P20 Numerical chaos
37B10 Symbolic dynamics
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37B30 Index theory for dynamical systems, Morse-Conley indices
37B55 Topological dynamics of nonautonomous systems

Software:

CAPD
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Full Text: DOI

References:

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