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Mathematics > Dynamical Systems
Title: A dynamical interpretation of the connection map of an attractor-repeller decomposition
(Submitted on 27 Mar 2024)
Abstract: In Conley index theory one may study an invariant set $S$ by decomposing it into an attractor $A$, a repeller $R$, and the orbits connecting the two. The Conley indices of $S$, $A$ and $R$ fit into an exact sequence where a certain connection homomorphism $\Gamma$ plays an important role. In this paper we provide a dynamical interpretation of this map. Roughly, $R$ "emits" an element of its Conley index as a "wavefront", part of which intersects the connecting orbits in $S$. This subset of the wavefront evolves towards $A$ and is then "received" by it to produce an element in its Conley index.
Submission history
From: Jaime Jorge Sánchez-Gabites [view email][v1] Wed, 27 Mar 2024 17:59:18 GMT (647kb)
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