Surfaces affines et germes tangents à l'identité

Some remarks on non-degenerate characteristic directions

12 juil. 2023, 10:30

50m

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

Orateur

Lorena Lopez-Hernanz

Description

Characteristic directions of a tangent to the identity biholomorphism $F$ in ${\mathbb{C}}^n$ are the only possible directions of tangency of an attracting orbit. Écalle and Hakim proved that every characteristic direction which satisfies a non-degeneracy assumption supports a parabolic curve, i.e. a 1-dimensional stable manifold for $F$ with 0 in its boundary; these parabolic curves can be seen as analytic sectorial realizations of a formal invariant object, which can be either a power series or a Dulac series. We will see how one could generalize Hakim's construction to obtain parabolic curves attached to more general formal invariant objects. This is a (very early stage) work in progress in collaboration with José Cano and Sergio Carrillo.