Tangent to the Identity Germs and Affine Surfaces

Projective structures on the n-punctured sphere and parabolic dynamics in (C3,0)

10 févr. 2025, 14:00

50m

Amphithéatre Schwartz (Institut de Mathématiques de Toulouse)

Orateur

Helena Reis

Description

There are at least two families of (Halphen) vector fields on ${\mathbb{C}}^3$ having a number of interesting properties. Among others, they induce projective structures on the 3 or 4 times punctured sphere and their dynamics is closely related to the dynamics of certain Fuchsian and Kleinian groups. Furthermore, they can be used to produce examples of tangent to the identity maps in $({\mathbb{C}}^3,0)$ whose dynamical study requires us to go slightly beyond the Fuchsian/Kleinian groups in question. I will try to explain this construction and say a few words about the structure of certain invariant sets.