A KAM-like theorem for normally hyperbolic quasi-periodic tori leading to efficient algorithms

CDSNS Colloquium
Monday, February 3, 2014 - 11:00am
1 hour (actually 50 minutes)
Univ. of Barcelona
We present a KAM-like theorem for the existence of quasi-periodic tori with a prescribed Diophantine rotation for a discrete family of dynamical system. The theorem is stated in an a posteriori format, so it can be used to validate numerical computations. The method of proof provides an efficient algorithm for computing quasi-periodic tori. We also present implementations of the algorithm, illustrating them throught several examples and observing different mechanisms of breakdown of qp invariant tori. This is a joint work with Alex Haro.