Sánchez Gabites, Jaime Jorge2026-02-192026-02-192025Sánchez-Gabites, J. J. A dynamical interpretation of the connection map of an attractor-repeller decomposition. Journal of Differential Equations 428 (2025): 688-720.0022-039610.1016/j.jde.2025.02.042https://hdl.handle.net/20.500.14352/132696Acuerdos transformativos CRUE 2025In 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessAttractor-repeller decompositionConley indexConnection homomorphismEcuaciones diferenciales1206.13 Ecuaciones Diferenciales en Derivadas Parciales