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arXiv · 1411.2945

Parabolic curves of diffeomorphisms asymptotic to formal invariant curves

Lorena López-Hernanz·Fernando Sanz Sánchez
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Abstract

We prove that if $F$ is a tangent to the identity diffeomorphism at $0\in\mathbb{C}^2$ and $\Gamma$ is a formal invariant curve of $F$ then there exists a parabolic curve (attracting or repelling) of $F$ asymptotic to $\Gamma$. The result is a consequence of a more general one in arbitrary dimension, where we prove the existence of parabolic curves of a tangent to the identity diffeomorphism $F$ at $0\in\mathbb{C}^n$ asymptotic to a given formal invariant curve under some additional conditions, expressed in terms of a reduction of $F$ to a special normal form by means of blow-ups and ramifications along the formal curve.

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Lorena López-Hernanz, Fernando Sanz Sánchez. 2014-11-11. Parabolic curves of diffeomorphisms asymptotic to formal invariant curves. https://doi.org/10.1515/crelle-2015-0064

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