On the Approximate Polar Curves of Foliations

Percy Fernández-Sánchez; Evelia R. García Barroso; Nancy Saravia-Molina

doi:10.3390/math11030613

On the Approximate Polar Curves of Foliations

Percy Fernández-Sánchez
, Evelia R. García Barroso
, Nancy Saravia-Molina

Sección de Matemáticas

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

1 Cita (Scopus)

Resumen

We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by García Barroso and Gwoździewicz for plane branches.

Idioma original	Inglés
Número de artículo	613
Publicación	Mathematics
Volumen	11
N.º	3
DOI	https://doi.org/10.3390/math11030613
Estado	Publicada - feb. 2023

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title = "On the Approximate Polar Curves of Foliations",

abstract = "We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by Garc{\'i}a Barroso and Gwo{\'z}dziewicz for plane branches.",

keywords = "characteristic approximate root, non-dicritical foliation, polar curve",

author = "Percy Fern{\'a}ndez-S{\'a}nchez and \{Garc{\'i}a Barroso\}, \{Evelia R.\} and Nancy Saravia-Molina",

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doi = "10.3390/math11030613",

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AU - García Barroso, Evelia R.

AU - Saravia-Molina, Nancy

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AB - We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by García Barroso and Gwoździewicz for plane branches.

KW - characteristic approximate root

KW - non-dicritical foliation

KW - polar curve

UR - https://www.scopus.com/pages/publications/85147868003

U2 - 10.3390/math11030613

DO - 10.3390/math11030613

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JO - Mathematics

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On the Approximate Polar Curves of Foliations

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