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Journal Articles Bulletin des Sciences Mathématiques Year : 2021

Pairs of foliations and Mattei-Moussu's Theorem

Abstract

We prove a reduction of singularities for pairs of foliations by blowing-up, and then investigate the analytic classification of the reduced models. Those reduced pairs of regular foliations are well understood. The case of a regular and a singular foliation is dealt with Mattei-Moussu's Theorem for which we provide a new proof, avoiding Gronwall's inequality. We end-up announcing results recently obtained by the first author in the case of a pair of reduced foliations sharing the same separatrices.
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Dates and versions

hal-02910135 , version 1 (31-07-2020)

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Adjaratou Arame Diaw, Frank Loray. Pairs of foliations and Mattei-Moussu's Theorem. Bulletin des Sciences Mathématiques, 2021, 171, pp.article n°103035. ⟨10.1016/j.bulsci.2021.103035⟩. ⟨hal-02910135⟩
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