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arXiv · 2302.10743

Rational Limit Cycles of Abel Differential Equations

José Luis Bravo Trinidad·Luis Ángel Calderón Pérez·Ignacio Ojeda Martínez de Castilla
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Abstract

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

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José Luis Bravo Trinidad, Luis Ángel Calderón Pérez, Ignacio Ojeda Martínez de Castilla. 2023-02-21. Rational Limit Cycles of Abel Differential Equations. https://arxiv.org/abs/2302.10743

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