# GDMSeminar: Abstracts of the Talks (2021/19)

**Luigi Chierchia **(Roma Tre)

*The ultimate frontier of KAM Theory (in finite dimensions) *

Tuesday, October 26, 2021, 15:00 GMT

**Abstract**: A fundamental question in KAM theory (which actually motivated Arnold's 1963 paper "Proof of a Theorem by A.N. Kolmogorov..."), is: what is the measure in phase space spanned by regular (quasi-periodic) motions? I will discuss recent results (joint with Luca Biasco), which show that, in the case of nearly-integrable generical mechanical systems, away from a "non perturbative set" around double resonances (i.e. a set in phase space where the motion is essentially described by a parameter-free Hamiltonian) of measure ~ O(ε), the phase space is filled by quasi-periodic motions up to a set exponentially small in 1/ε