On the Approximate Polar Curves of Foliations

  1. Fernández-Sánchez, Percy 2
  2. García Barroso, Evelia R. 1
  3. Saravia-Molina, Nancy 2
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

  2. 2 Pontificia Universidad Católica del Perú
    info

    Pontificia Universidad Católica del Perú

    Lima, Perú

    ROR https://ror.org/00013q465

Journal:
Mathematics

ISSN: 2227-7390

Year of publication: 2023

Volume: 11

Issue: 3

Pages: 613

Type: Article

DOI: 10.3390/MATH11030613 GOOGLE SCHOLAR lock_openOpen access editor

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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.