Résonance 1 : 2 pour les champs de vecteurs réversibles

We study the 1:2 resonance for reversible vector fields in $\text{R}{}^4$, depending on a parameter μ and we show the bifurcation of two families of periodic solutions and of two reversible solutions which are homoclinic to some of the periodic solutions belonging to one or the other of the previous families, depending on the sign of a coefficient. To cite this article: M. Barrandon, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 7–10