Surfaces affines et germes tangents à l'identité

Local dynamics of skew-products tangent to the identity

12 juil. 2023, 14:00

50m

Salle K. Johnson (1R3-1er étage) (Institut de Mathématiques)

Orateur

Matthieu Astorg

Description

The results we will present in this talk deal with local dynamics of skew-products $P$ with a (non-degenerate) tangent to the identity fixed point at the origin. We will give an explicit sufficient condition on its coefficients for $P$ to have wandering Fatou components. In particular, we will see that the dynamics of quadratic maps of the form $(z,w)\mapsto (z-z^2,w+w^2+b{z}^2)$ is surprisingly rich: under an explicit arithmetic condition on $b$, these maps have an infinity of grand orbits of wandering Fatou components, all of which admit non-constant limit maps. The main technical result is a parabolic implosion-type theorem, in which the renormalization limits that appear are different from previously known cases.

Travail en collaboration avec Luka Boc Thaler