English

Rational Limit Cycles of Abel Differential Equations

Classical Analysis and ODEs 2023-02-22 v1

Abstract

We study the number of rational limit cycles of the Abel equation x=A(t)x3+B(t)x2x'=A(t)x^3+B(t)x^2, where A(t)A(t) and B(t)B(t) are real trigonometric polynomials. We show that this number is at most the degree of A(t)A(t) plus one.

Keywords

Cite

@article{arxiv.2302.10743,
  title  = {Rational Limit Cycles of Abel Differential Equations},
  author = {José Luis Bravo Trinidad and Luis Ángel Calderón Pérez and Ignacio Ojeda Martínez de Castilla},
  journal= {arXiv preprint arXiv:2302.10743},
  year   = {2023}
}