<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 [<bold>Lo</bold>], 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.</p>
</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.

Characterization of second type plane foliations using Newton polygons

Pontificia Universidad Católica del Perú

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Characterization of second type plane foliations using Newton polygons"}

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...

Characterization of second type plane foliations using Newton polygons

Published Online: Jun 02, 2022

Page range: 103 - 123

Received: Jul 06, 2021

Accepted: Sep 30, 2021

DOI: https://doi.org/10.2478/auom-2022-0021

Keywords
foliation, second type foliation, Newton polygon

© 2022 Percy Fernández-Sánchez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Characterization of second type plane foliations using Newton polygons

Published Online: Jun 02, 2022

Page range: 103 - 123

Received: Jul 06, 2021

Accepted: Sep 30, 2021

DOI: https://doi.org/10.2478/auom-2022-0021

Keywordsfoliation, second type foliation, Newton polygon

© 2022 Percy Fernández-Sánchez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
foliation, second type foliation, Newton polygon