J. L. Bravo

collaborators

4 papers

math.DS2023

Quartic rigid systems in the plane and in the Poincaré sphere

M. J. Álvarez, J. L. Bravo, L. A. Calderón

We consider the planar family of rigid systems of the form $x^{'} = - y + x P (x, y), y^{'} = x + y P (x, y)$ , where $P$ is any polynomial with monomials of degree one and three. This is the simplest n…

math.DS2023

Hilbert number for a family of piecewise nonautonomous equations

J. L. Bravo, M. Fernandez, I. Ojeda

For family $x^{'} = (a_{0} + a_{1} cos t + a_{2} sin t) ∣ x ∣ + b_{0} + b_{1} cos t + b_{2} sin t$ , we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poinc…

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…