FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 53-64

Theorem on the density of separatrix connections for polynomial foliations in $$CP²

D. S. Volk

Abstract

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In this paper, we prove that in the space of polynomial foliations of a fixed degree of the complex two-dimensional space, foliations with separatrix connection, i.e., foliations in which any two distinct point have a common separatrix, are dense. The main tool of the proof is the analysis of the monodromy group of the foliation in a neighborhood of the infinitely distant point of the ambient projective space.

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Last modified: February 17, 2007