Geodesic
Limit cycles for vector fields with homogeneous components
Applicationes Mathematicae, Tome 24 (1997) no. 3, pp. 281-287

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study planar polynomial differential equations with homogeneous components. This kind of equations present a simple and well known dynamics when the degrees (n and m) of both components coincide. Here we consider the case $n\ne m$ and we show that the dynamics is more complicated. In fact, we prove that such systems can exhibit periodic orbits only when nm is odd. Furthermore, for nm odd we give examples of such differential equations with at least (n+m)/2 limit cycles.
DOI : 10.4064/am-24-3-281-287
Keywords: homogeneous function, limit cycle, vector field

A. Cima 1 ; A. Gasukk 1 ; F. Mañosas 1

1 
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A. Cima; A. Gasukk; F. Mañosas. Limit cycles for vector fields with homogeneous components. Applicationes Mathematicae, Tome 24 (1997) no. 3, pp. 281-287. doi: 10.4064/am-24-3-281-287

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