no. 5
Instability of equilibria in dimension three
Annales de l'Institut Fourier, Tome 48 (1998) no. 5, pp. 1345-1357.

Dans cet article on démontre que si v est un champ de vecteurs analytique sur ℝ 3 ayant une singularité isolée en 0, alors il existe une trajectoire de v qui tend vers 0 dans le passé ou dans le futur. La preuve repose sur certains résultats concernant la désingularisation des champs de vecteurs en dimension trois et sur des arguments d’indice à la Poincaré-Hopf.

In this paper we show that if v is an analytic vector field on ℝ 3 having an isolated singular point at 0, then there exists a trajectory of v which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments à la Poincaré-Hopf.

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     author = {Brunella, Marco},
     title = {Instability of equilibria in dimension three},
     journal = {Annales de l'Institut Fourier},
     pages = {1345--1357},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {5},
     year = {1998},
     doi = {10.5802/aif.1657},
     mrnumber = {99i:34040},
     zbl = {0930.37025},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1657/}
}
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Brunella, Marco. Instability of equilibria in dimension three. Annales de l'Institut Fourier, Tome 48 (1998) no. 5, pp. 1345-1357. doi : 10.5802/aif.1657. http://www.numdam.org/articles/10.5802/aif.1657/

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