Sliding invariant and classification of singular holomorphic foliations in the plane

Sliding invariant and classification of singular holomorphic foliations in the plane

By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will show that, in this class, the new invariant is finitely determi...

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Veröffentlicht in:Annales de l'Institut Fourier 2015, Vol.tome 65 (5), p.1897-1920
1. Verfasser: Truong, Hong Minh
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Sprache:eng
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Dynamical Systems
Mathematics
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container_end_page 1920
container_issue 5
container_start_page 1897
container_title Annales de l'Institut Fourier
container_volume tome 65
creator Truong, Hong Minh
description By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will show that, in this class, the new invariant is finitely determined. Consequently, the finite determination of the class of isoholonomy non-dicritical foliations and absolutely dicritical foliations that have the same Dulac maps are proved.
doi_str_mv 10.5802/aif.2976
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subjects Dynamical Systems
Mathematics
title Sliding invariant and classification of singular holomorphic foliations in the plane
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