AM550: Problemi di piccoli divisori
Dynamical systems and vector fields on finite and infinite
dimensional Hilbert spaces. Vector fields as derivations, push-forward
of a vector field, Lie derivative, the
Lie exponentiation formula. Symmetries and constants of motion.
Reducibility of linear quasi-periodically forced systems. Finite and
infinite dimensional case. Hamiltonian vector fields on a finite
and infinite dimensional Hilbert space.
Hamiltonian formalism, symplectic changes of variables. Analytic
Hamiltonians, regular Hamiltonians, norms and Cauchy
estimates. Polynomial hamiltonians and degree decomposition.
KAM theory for finite dimensional tori: maximal tori, elliptic tori.
Moser- Zehnder: Notes on dynamical systems.