Stable manifolds for germs of biholomorphisms asymptotic to formal curves
Thursday, 18. February 2021, 16:00 - 17:00
Hits : 69
Contact Lorena López Hernanz (Universidad de Alcalá)
Abstract
We study the existence of stable manifolds for germs of biholomorphisms in $C^n, n>1$. We will show that if there exists a formal invariant curve for the biholomorphism (a condition that always holds in dimension two) and the restriction to that curve has an attracting behavior (i.e. the multiplier of the restriction is hyperbolic attracting or is a root of unity) then there exist stable manifolds where all the orbits are asymptotic to the formal curve. In the particular case of dimension two, we will show how this result allows to obtain a more general condition for the existence of stable manifolds.
The first part of the talk is based on two joint works with F. Sanz, J. Raissy, J. Ribón and L. Vivas; the second part, on one with R. Rosas.
Location on-line