| Contents |
| KAM theory deals with the existence and persistence of invariant tori carrying quasi-periodic motion. Nowadays, KAM theory is
a vast area of research that involves a large collection of methods and applications. The parametrization method, introduced during the last decade by Rafael de la Llave and collaborators, consists in adding a small function to a parametrization of an approximately invariant torus. This function is obtained by approximately solving the linearized invariance equation around the approximated torus (Newton-like iterative scheme). The approach is suitable for studying existence of invariant tori without using neither action-angle variables nor a perturbative setting.
In this talk we present a KAM theorem using a common frame that unifies several works in the literature. We will consider some academic examples (the standard map and the Froeschle map) to illustrate the application of the result for specific values of the perturbation parameter (i.e. not arbitrarily small). Then, we will discuss how this methodology allows us to obtain invariant tori in a non-perturbative setting using computer-aided-methods. |
|