Tangent to the Identity Germs and Affine Surfaces

Local dynamics of reduced saddle-node biholomorphisms

12 févr. 2025, 11:20

50m

Amphithéatre Schwartz (Institut de Mathématiques de Toulouse)

Orateur

Liz Vivas

Description

We study the dynamics on a full neighborhood of the origin for a biholomorphism $F$ in ${\mathbb{C}}^2$ that is of the reduced saddle-node type. For these type of diffeomorphisms we will show that there exist connected domains with the origin in their boundary which are either stable for $F$ or for its inverse, and that outside these domains every point is either fixed or has a finite orbit. This is a work in progress in collaboration with Lorena Lopez-Hernanz and Rudy Rosas.