Tangent to the Identity Germs and Affine Surfaces

Local dynamics of biholomorphisms (2)

11 févr. 2025, 09:00

1h

Amphithéatre Schwartz (Institut de Mathématiques de Toulouse)

Orateur

Xavier Buff (Institut de Mathématiques de Toulouse)

Description

The goal of this series of lecture is to present the relation between the dynamics of germs $f:({\mathbb{C}}^2,0)\to ({\mathbb{C}}^2,0)$ tangent to the identity, the real-time dynamics of homogeneous vector fields in ${\mathbb{C}}^2$ and the dynamics of the geodesic flow on affine surfaces.

In the second lecture, we will explain how, to each germ $f:({\mathbb{C}}^2,0)\to ({\mathbb{C}}^2,0)$ tangent to the identity, one can associate a homogeneous vector field in ${\mathbb{C}}^2$ and a meromorphic affine surface modeled on the Riemann sphere minus finitely many points.