Computer assisted proofs in KAM theory

CDSNS Colloquium
Monday, April 6, 2015 - 11:00am
1 hour (actually 50 minutes)
Skiles 005
Univ. of Barcelona
We present a methodology to rigorously validate a given approximation of a quasi-periodic Lagrangian torus of a symplectic map. The approach consists in verifying the hypotheses of a-posteriori KAM theory based of the parameterization method (following Rafael de la Llave and collaborators). A crucial point of our imprementation is an analytic Lemma that allows us to control the norm of periodic functions using their discrete Fourier transform. An outstanding consequence of this approach it that the computational cost of the validation is assymptotically equivalent of the cost of the numerical computation of invariant tori using the parametererization method. We pretend to describe some technical aspects of our implementation. This is a work in progress joint with Jordi-Lluis Figueras and Alejandro Luque.