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Nilpotent singularities and first integrals. (Singularités nilpotentes et intégrales premières.) (French. English summary) Zbl 1134.32306

Summary: This paper presents a classification of plane dicritical nilpotent singularities, i.e. singularities which have nilpotent linear part and infinitely many separatrices. In particular the existence of meromorphic first integrals is discussed. The same ideas are applied to other kind of dicritical singularities.

MSC:

32S65 Singularities of holomorphic vector fields and foliations
37F75 Dynamical aspects of holomorphic foliations and vector fields
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