Dia: Dimecres, 28 d'octubre de 2020
Lloc: ONLINE https://eu.bbcollab.com/guest/e72c23cf69754e1ca7555595a9a0f2bf
A càrrec de: Clara Cufí Cabrè, Universitat Autònoma de Barcelona
Títol: Differentiable invariant manifolds of nilpotent parabolic points
Resum: We consider a map F of class 𝒞r with a fixed point of parabolic type whose differential is not diagonalizable and we study the existence and regularity of the invariant manifolds associated with the fixed point using the parameterization method. Concretely, we show that under suitable conditions on the coefficients of F, there exist invariant curves of class 𝒞r away from the fixed point, and that they are analytic when F is analytic. The differentiability result is obtained as an application of the fiber contraction theorem. We also provide an algorithm to compute an approximation of a parameterization of the invariant curves and a normal form of the restricted dynamics of F on them.
This is a joint work with Ernest Fontich (Universitat de Barcelona).
Last updated: Fri Oct 23 12:52:51 2020