Construction of quasi-periodic solutions of State-dependent delay differential equations by the parameterization method II: Details.

Dynamical Systems Working Seminar
Tuesday, September 15, 2015 - 5:00pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech (Math)/Hunan University
We investigate the existence of quasi-periodic solutions for state-dependent delay differential equationsusing the parameterization method, which is different from the usual way-working on the solution manifold.  Under the assumption of finite-time differentiability of functions and exponential dichotomy, the existence and smoothness of quasi-periodic solutions are investigated by using contraction arguments We also develop a  KAM theory  to seek analytic quasi-periodic solutions. In contrast with the finite differentonable theory, this requires adjusting parameters. We prove that the set of parameters which guarantee the existence of analytic quasi-periodic solutions is of positive measure. All of these results are given in an a-posterior form. Namely, given a approximate solution satisfying some non-degeneracy conditions, there is a true solution nearby.