%0 Journal Article
%A Sánchez Gabites, Jaime Jorge
%T A dynamical interpretation of the connection map of an attractor-repeller decomposition
%D 2025
%@ 0022-0396
%U https://hdl.handle.net/20.500.14352/132696
%X 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 Γ 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.
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