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 second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincar´e-Hopf index. This...

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Detalles Bibliográficos
Autores: García Barroso, Evelia Rosa, Fernández Sánchez, Percy, Saravia Molina, Nancy
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad de La Laguna (ULL)
Repositorio:RIULL. Repositorio Institucional de la Universidad de La Laguna
OAI Identifier:oai:riull.ull.es:915/41027
Acceso en línea:http://riull.ull.es/xmlui/handle/915/41027
Access Level:acceso abierto
Palabra clave:foliation
second type foliation
Newton polygon
Descripción
Sumario: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 Poincar´e-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.