Exceptional hyperbolic CR-singularities and reversible parabolic diffeomorphisms of (C2,0)

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

vendredi 2 févr. 2024, 10:30 → 11:30 Europe/Paris

207 (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.