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arXiv · 1803.01954

Characteristic directions of two-dimensional biholomorphisms

Lorena López-Hernanz·Rudy Rosas
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Abstract

We prove that for each characteristic direction $[v]$ of a tangent to the identity diffeomorphism of order $k+1$ in $\mathbb{C}^2$ there exist either an analytic curve of fixed points tangent to $[v]$ or $k$ parabolic manifolds where all the orbits are tangent to $[v]$, and that at least one of these parabolic manifolds is or contains a parabolic curve.

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Lorena López-Hernanz, Rudy Rosas. 2018-03-05. Characteristic directions of two-dimensional biholomorphisms. https://doi.org/10.1112/s0010437x20007071

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