Theorem on the density of separatrix connections for polynomial foliations in ℂP
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Authors: | D S Volk |
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Institution: | (1) M. V. Lomonosov Moscow State University, Russia |
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Abstract: | 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 points 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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 53–64, 2006. |
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