Under fairly general hypotheses, we prove the existence of the families of periodic orbits obtained by Hopf bifurcation, with emphasis on their smoothness. A Banach version of a theorem of Lyapounov is obtained as a corollary. The proofs are complete, simple and original.
Sous des hypothèses très générales, nous prouvons l'existence des familles d'orbites périodiques obtenues par bifurcation de Hopf, en insistant sur leur régularité. Nous en déduisons une version banachique d'un théorème de Lyapounov. Les démonstrations sont complètes, simples et originales.
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Marc Chaperon 1; Santiago López de Medrano 2
@article{CRMATH_2005__340_11_833_0, author = {Marc Chaperon and Santiago L\'opez de Medrano}, title = {On the {Hopf} bifurcation for flows}, journal = {Comptes Rendus. Math\'ematique}, pages = {833--838}, publisher = {Elsevier}, volume = {340}, number = {11}, year = {2005}, doi = {10.1016/j.crma.2005.04.006}, language = {en}, }
Marc Chaperon; Santiago López de Medrano. On the Hopf bifurcation for flows. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 833-838. doi : 10.1016/j.crma.2005.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.006/
[1] M. Chaperon, S. López de Medrano, J.L. Samaniego. On sub-harmonic bifurcations. C. R. Acad. Sci. Paris, Ser. I 304 (2005), in press
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