I. Ojeda

collaborators

5 papers

math.DS2025

Upper bound for the number of limit cycles for symmetric piecewise linear differential equations with three zones

J. L. Bravo, V. Carmona, M. Fernández +1

The study of the periodic dynamics of the family of continuous observable and non-controllable three-dimensional symmetric piecewise linear systems with three zones considered here…

math.AC2023

Minimal free resolution of generalized repunit algebras

Isabel Colaço, Ignacio Ojeda

Let $k$ be an arbitrary field and let $b > 1, n > 1$ and $a$ be three positive integers. In this paper we explicitly describe a minimal $S -$ graded free resolution of the semigr…

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…