A dynamical interpretation of the connection map of an attractor-repeller decomposition
Dynamical Systems
2024-03-28 v1
Abstract
In Conley index theory one may study an invariant set by decomposing it into an attractor , a repeller , and the orbits connecting the two. The Conley indices of , and fit into an exact sequence where a certain connection homomorphism plays an important role. In this paper we provide a dynamical interpretation of this map. Roughly, "emits" an element of its Conley index as a "wavefront", part of which intersects the connecting orbits in . This subset of the wavefront evolves towards and is then "received" by it to produce an element in its Conley index.
Keywords
Cite
@article{arxiv.2403.18815,
title = {A dynamical interpretation of the connection map of an attractor-repeller decomposition},
author = {J. J. Sánchez-Gabites},
journal= {arXiv preprint arXiv:2403.18815},
year = {2024}
}