course: The KAM theorem, following the original approach designed by Kolmogorov

speaker: Ugo Locatelli (Dip. di Matematica dell'Universita' di Roma "Tor Vergata")

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.

Contents of the lectures

timetable:
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
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