KAM (Kolmogorov-Arnold-Moser) Theory (171530)

The first lecture takes place at the 20th of November from 4:00 pm to 5:30 pm in room E 2.304.

Lecture (Di Gregorio):

Description of the course:
Within Dynamical Systems a special place is taken up by Hamiltonian Systems. In this field KAM (Kolmogorov-Arnold-Moser) Theory plays an essential role. This Theory is not a collection of specific theorems but rather a methodology, a collection of ideas of how to approach certain problems in perturbation theory connected with "small divisors". The aim of these lectures is to describe the KAM Theorem on the conservation of invariant tori in its basic form and to give a complete and detailed proof of it. This proof essentially follows the traditional line laid out by Kolmogorov (1954) giving more emphasis on the underlying ideas than on the sharpness of the arguments.

Prerequisites: basic facts on Hamiltonian systems.

Contents:
symplectic structure on a manifold; Hamilton's equations; generating function; action-angles variables (Arnold-Jost Theorem); introduction to the classical KAM Theory; Perturbation Theory (examples); Kolmogorov's Theorem with complete proof.