KAM Theory without Action-angle Variables and its Extension to Presymplectic Dynamical Systems

Dynamical Systems Working Seminar
Tuesday, September 1, 2015 - 17:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
We will discuss KAM results for symplectic and presymplectic maps. Firstly, we will study geometric properties of a symplectic dynamical system which will allow us to prove a KAM theorem in a-posteriori format. Then, a corresponding theorem for a parametric family of symplectic maps will be presented. Finally, using similar method, we will extend the theorems to presymplectic maps. These results appear in the work of Alishah, de la Llave, Gonzalez, Jorba and Villanueva.