J. L. Bravo

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math.CA2023

Stability of singular limit cycles for Abel equations revisited

J. L. Bravo, M. Fernández, I. Ojeda

A criterion is obtained for the semi-stability of the isolated singular positive closed solutions, i.e., singular positive limit cycles, of the Abel equation $x^{'} = A (t) x^{3} + B (t) x^{2}$ ,…

math.CA2023

Rational Limit Cycles of Abel Differential Equations

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

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 m…