Persistence of Invariant Objects in Functional Differential Equations close to ODEs

Abstract: We consider functional differential equations which are perturbations of ODEs in $\mathbb{R}^n$. This is a singular perturbation problem even for small perturbations. We prove that for small enough perturbations, some invariant objects of the unperturbed ODEs persist and depend on the parameters with high regularity. We formulate a-posteriori type of results in the case when the unperturbed equations admit periodic orbits. The results apply to state-dependent delay equations and equations which arise in the study of electrodynamics. The proof is constructive and leads to an algorithm. This is a joint work with Joan Gimeno and Rafael de la Llave.

mathematical physicsanalysis of PDEs

Audience: researchers in the topic

TAMU: Mathematical Physics and Harmonic Analysis Seminar