2 results
Characteristic directions of two-dimensional biholomorphisms
- Part of
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- Journal:
- Compositio Mathematica / Volume 156 / Issue 5 / May 2020
- Published online by Cambridge University Press:
- 31 March 2020, pp. 869-880
- Print publication:
- May 2020
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- Article
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We prove that for each characteristic direction
$[v]$ of a tangent to the identity diffeomorphism of order 
$k+1$ in 
$(\mathbb{C}^{2},0)$ 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.
Invariant sets near singularities of holomorphic foliations
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 36 / Issue 8 / December 2016
- Published online by Cambridge University Press:
- 21 July 2015, pp. 2408-2418
- Print publication:
- December 2016
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- Article
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Consider a complex one-dimensional foliation on a complex surface near a singularity
$p$. If 
${\mathcal{I}}$ is a closed invariant set containing the singularity 
$p$, then 
${\mathcal{I}}$ contains either a separatrix at 
$p$ or an invariant real three-dimensional manifold singular at 
$p$.
