Pairs of foliations and Mattei-Moussu's theorem
Classical Analysis and ODEs
2020-08-04 v1
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.
Keywords
Cite
@article{arxiv.2008.00719,
title = {Pairs of foliations and Mattei-Moussu's theorem},
author = {Adjaratou Arame Diaw and Frank Loray},
journal= {arXiv preprint arXiv:2008.00719},
year = {2020}
}