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arXiv · 1901.05565

Conley's index and connection matrices for non-experts

Phillipo Lappicy
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Abstract

This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the necessary topological background, before we proceed to the basic properties of the index. Then, the itinerary passes through the construction of connection matrices with a panoramic view of the applications: detect heteroclinic orbits arising in delay differential equations, and partial differential equations of parabolic type. The ride will be filled with examples and figures.

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Phillipo Lappicy. 2019-01-17. Conley's index and connection matrices for non-experts. https://arxiv.org/abs/1901.05565

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