Persistence of Invariant Objects under Delay Perturbations

Series
Dissertation Defense
Time
Thursday, May 6, 2021 - 4:00pm for 1 hour (actually 50 minutes)
Location
ONLINE at https://bluejeans.com/137621769
Speaker
Jiaqi Yang – Georgia Tech
Organizer
Jiaqi Yang

 We consider functional differential equations which come from adding delay-related perturbations to ODEs or evolutionary PDEs, which is a singular perturbation problem. We prove that for small enough perturbations, some invariant objects (e.g. periodic orbits, slow stable manifolds) of the unperturbed equations persist and depend on the parameters with high regularity. The results apply to state-dependent delay equations and equations which arise in electrodynamics. We formulate results in a posteriori format. The proof is constructive and leads to algorithms. 

This is based on joint works with Joan Gimeno and Rafael de la Llave.

Link: https://bluejeans.com/137621769