Orateur
Description
Let $F:(\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ be a germ of a holomorphic diffeomorphism and let $\Gamma$ be a formal curve at $0$, invariant for $F$. Under certain sharp conditions on the restricted diffeomorphism $F|_\Gamma$, we show that there exists a finite non-empty family of complex submanifolds of $\mathbb{C}^n\setminus\{0\}$, invariant for $F$ and entirely composed of orbits which converge to the origin and have flat contact with $\Gamma$ (parabolic manifolds). In a second part of the talk, we adapt this result for the case of a germ of a real analytic diffeomorphism $F:(\mathbb{R}^n,0)\to(\mathbb{R}^n,0)$, where we can show, moreover, that each parabolic manifold of the family is foliated by real parabolic curves of $F$.
These results are obtained in collaboration with L. López-Hernánz, J. Ribón, J. Raissy and L. Vivas.
