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Characterization of second type plane foliations using Newton polygons Cover

Abstract

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same process of singularity reduction that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

DOI: https://doi.org/10.2478/auom-2022-0021 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 103 - 123
Submitted on: Jul 6, 2021
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Accepted on: Sep 30, 2021
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Published on: Jun 2, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2022 Percy Fernández-Sánchez, Evelia R. García barroso, Nancy Saravia-Molina, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.