Invariant sets near singularities of holomorphic foliations

César Camacho; Rudy Rosas

doi:10.1017/etds.2015.23

Invariant sets near singularities of holomorphic foliations

César Camacho
, Rudy Rosas

Sección de Matemáticas

Instituto National de Matemática Pura e Aplicada
Instituto de Matemática y Ciencias Afines

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Consider a complex one-dimensional foliation on a complex surface near a singularity p. If I is a closed invariant set containing the singularity p, then I contains either a separatrix at p or an invariant real three-dimensional manifold singular at p.

Original language	English
Pages (from-to)	2408-2418
Number of pages	11
Journal	Ergodic Theory and Dynamical Systems
Volume	36
Issue number	8
DOIs	https://doi.org/10.1017/etds.2015.23
State	Published - 1 Dec 2016

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title = "Invariant sets near singularities of holomorphic foliations",

abstract = "Consider a complex one-dimensional foliation on a complex surface near a singularity p. If I is a closed invariant set containing the singularity p, then I contains either a separatrix at p or an invariant real three-dimensional manifold singular at p.",

author = "C{\'e}sar Camacho and Rudy Rosas",

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AU - Camacho, César

AU - Rosas, Rudy

N1 - Publisher Copyright: © Cambridge University Press, 2015.

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Y1 - 2016/12/1

N2 - Consider a complex one-dimensional foliation on a complex surface near a singularity p. If I is a closed invariant set containing the singularity p, then I contains either a separatrix at p or an invariant real three-dimensional manifold singular at p.

AB - Consider a complex one-dimensional foliation on a complex surface near a singularity p. If I is a closed invariant set containing the singularity p, then I contains either a separatrix at p or an invariant real three-dimensional manifold singular at p.

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DO - 10.1017/etds.2015.23

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JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

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Invariant sets near singularities of holomorphic foliations

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