Decomposition of two dimensional real analytic diffeomorphisms and applications

par Maria Martin (Université de Valladolid)

vendredi 4 avr. 2025, 10:30 → 11:30 Europe/Paris

Given a germ of a two dimensional real analytic diffeomorphism of non center-focus type, there is a neighborhood of the origin and a stratification of it into invariant manifolds, on which the asymptotic dynamics of the diffeomorphism are uniformly determined. This work particularizes the ${\mathcal{C}}^{\mathrm{\infty }}$ decomposition of Dumortier-Rodrigues-Roussarie to the analytic case, avoiding some hypotheses. In particular, we consider the presence of curves of fixed points. We will give some applications of this result to three dimensional vector fields.