Georgia Institute of Technology College of Sciences

A fundamental question in Dynamical Systems is to identify regions of
phase/parameter space satisfying a given property (stability,
linearization, etc).  In this talk, given a family of analytic circle
diffeomorphisms depending on a parameter, we obtain effective (almost
optimal) lower bounds of the Lebesgue measure of the set of parameters
for which that diffeomorphism is conjugate to a rigid rotation.
We estimate this measure using an a-posteriori KAM
scheme that relies on quantitative conditions that
are checkable using computer-assistance. We carefully describe
how the hypotheses in our theorems are reduced to a finite number of
computations, and apply our methodology to the case of the
Arnold family, in the far-from-integrable regime.

This is joint work with Jordi Lluis Figueras and Alejandro Luque.