### Effective bounds for the measure of rotations

- Series
- CDSNS Colloquium
- Time
- Monday, October 28, 2019 - 11:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 05
- Speaker
- Alex Haro – Univ. de Barcelona

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.