On the Approximate Polar Curves of Foliations

Percy Fernández-Sánchez, Evelia R. García Barroso and Nancy Saravia-Molina ()
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Percy Fernández-Sánchez: Departamento Ciencias—Sección Matemáticas, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel 15088, Lima, Peru
Evelia R. García Barroso: Departamento Matemáticas, Estadística e I.O. Sección de Matemáticas, Universidad de La Laguna, Apartado de Correos 456, 38200 La Laguna, Tenerife, Spain
Nancy Saravia-Molina: Departamento Ciencias—Sección Matemáticas, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel 15088, Lima, Peru

Mathematics, 2023, vol. 11, issue 3, 1-25

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 García Barroso and Gwoździewicz for plane branches.

Keywords: non-dicritical foliation; polar curve; characteristic approximate root (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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