DOI: https://doi.org/10.15446/recolma.v49n2.60443

On the limit cycles of quasihomogeneous polynomial systems

Sobre los ciclos límite de sistemas polinomiales cuasi-homogeneos

L. Rocío González-Ramírez^1,2, Osvaldo Osuna^1,*, Rubén Santaella-Forero¹

¹ Universidad Michoacana de San Nicolás de Hidalgo, Morelia, México
e-mail: rgonzalez@ifm.umich.mx
e-mail: osvaldo@ifm.umich.mx
² Catedrática CONACYT, D.F., México
e-mail: rusanfo@matmor.unam.mx

Abstract

In this work, the nonexistence of limit cycles for classes of p − q quasi-homogeneous polynomial planar systems of weighted degree l is established. Furthermore, we rule out the existence of limits cycles for certain perturbations of such planar systems. We present applications and examples in order to illustrate our results.

Key words and phrases. Integrating factors, Inverse integrating factors, Limit cycles, p − q-quasi-homogeneous systems.

2010 Mathematics Subject Classification. 34C05, 34C07, 34C25.

Resumen

En este trabajo, se establece la no existencia de ciclos límite para la clase de sistemas bidimensionales, polinomiales p − q-cuasi-homogeneos de grado ponderado l. Además, se descarta la existencia de ciclos límite para ciertas perturbaciones de tales sistemas. Finalmente, se presentan aplicaciones y ejemplos para ilustrar los resultados obtenidos.

Palabras y frases clave. Factores Integrantes, Factores integrantes inversos, ciclos límite, sistemas p − q-cuasi-homogeneos.

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(Recibido en marzo de 2015. Aceptado en octubre de 2015)