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On the Approximate Polar Curves of Foliations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Percy Fernández-Sánchez & Evelia R. García Barroso & Nancy Saravia-Molina, 2023. "On the Approximate Polar Curves of Foliations," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:613-:d:1047072
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