2024/03/27 by J. J. Sánchez-Gabites, Sánchez-Gabites, J. J.
Engineering · Physics and Astronomy · #37B30 #37B35 #55N99 #Adaptive Control of Nonlinear Systems #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Guidance and Control Systems
paper · pdf · doi:10.48550/arxiv.2403.18815
openalex publication_date 2024/03/27 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28
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.