Invariant manifolds for parabolic nilpotent fixed points [ Back ]

Date:
17.12.18   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Clara Cufí
University:
Universitat Autònoma de Barcelona

Abstract

We consider a discrete dynamical system in the plane defined by an analytic map having a parabolic fixed point with nilpotent component. We will prove the existence of an analytic stable curve associated to such a fixed point using the parameterization method for invariant manifolds. The proof that we will present brings some advantages to the previous ones: it allows to give the result of existence as an "a posteriori theorem" and also it allows to determine an explicit algorithm to compute an approximation of the invariant curve. The talk is based on the results of the master thesis "The parameterization method for invariant curves associated to parabolic points" performed under the supervision of Ernest Fontich