**abstract:**

Program:

- Setting of perturbation theory in the Hamiltonian framework: Poisson brackets, canonical transformations, Lie series, quasi-integrable systems, short discussion about the Poincare's theorem of non-existence of first integrals.

- Main ideas behind the KAM theorem: Diophantine non-resonance condition, the Kolmogorov normal form, quasi-periodic flow on invariant tori, the formal algorithm constructing the Kolmogorov normal form.

- Introduction of some essential technical tools: complex domains for analytic functions and suitable Cauchy-Fourier estimates for Lie series.

- A complete proof of the KAM theorem, based on the Kolmogorov normalization scheme and using the Lie series method.

- KAM theorem and its neighborhood: relative measure of the persistent invariant tori, sketch of the proof scheme designed by Arnold, lower dimensional invariant tori of elliptic type.

Mon 3 Sep, 8:30 - 10:30, Aula Dini

Wed 5 Sep, 8:30 - 10:30, Aula Dini

Fri 7 Sep, 8:30 - 10:30, Aula Dini

Fri 7 Sep, 14:30 - 16:30, Aula Dini

<< Go back