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Invariant sets near singularities of holomorphic foliations

Published online by Cambridge University Press:  21 July 2015

CÉSAR CAMACHO  and
RUDY ROSAS
CÉSAR CAMACHO
Affiliation:
IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil email [email protected]
RUDY ROSAS
Affiliation:
Pontificia Universidad Católica del Perú, Av Universitaria 1801, Lima, Peru Instituto de Matemática y Ciencias Afines, Jr. los biólogos 245, Lima, Peru email [email protected]
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Abstract

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 $p$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 8 , December 2016 , pp. 2408 - 2418
Copyright
© Cambridge University Press, 2015 

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