Séminaire de Systèmes Dynamiques

Exceptional hyperbolic CR-singularities and reversible parabolic diffeomorphisms of $(\mathbb{C}2,0)$

by Laurent Stolovitch (Laboratoire J.A. Dieudonné, Nice)

207 (Bat 1R2)


Bat 1R2


In this joint work with Martin Klimes, we solve the problem of both formal and analytic classification of germs of real analytic surfaces in $(\mathbb{C}^2$ with  CR singularities of exceptional hyperbolic type, under the assumption that the surface is holomorphically flat, i.e. that it can be locally holomorphically embedded in a real hypersurface of $(\mathbb{C}^2$. It happens that this relies on the study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point at the origin.