Davoud Cheraghi (Munich)
On a conjecture of Marmi, Moussa, and Yoccoz on the sizes of
Quasi-periodic dynamics in one complex variable reveal
fascinating interplays between
complex analysis and Diophantine approximations. The question of whether
dynamic is conjugate to an irrational rotation dates back to more than a
with remarkable contributions by C. Siegel, A. Brjuno, and J.-C. Yoccoz.
The maximal domain on which a conjugacy exists is called the Siegel disk
of the map, and it is known
that the size of the Siegel disk is given by an arithmetic function of
the rotation, up to an error function.
In 1992, Marmi, Moussa, and Yoccoz conjectured that the error function
is 1/2-holder continuous.
In this talk, I will discuss a major advance on this conjecture, using a
acting on an infinite dimensional space of maps. This is based on a
joint work with Arnaud Cheritat (Toulouse).