In this paper we show that if is an analytic vector field on having an isolated singular point at 0, then there exists a trajectory of 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.
Dans cet article on démontre que si est un champ de vecteurs analytique sur ayant une singularité isolée en 0, alors il existe une trajectoire de 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.
@article{AIF_1998__48_5_1345_0, 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}, zbl = {0930.37025}, mrnumber = {99i:34040}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1657/} }
TY - JOUR AU - Brunella, Marco TI - Instability of equilibria in dimension three JO - Annales de l'Institut Fourier PY - 1998 SP - 1345 EP - 1357 VL - 48 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1657/ DO - 10.5802/aif.1657 LA - en ID - AIF_1998__48_5_1345_0 ER -
%0 Journal Article %A Brunella, Marco %T Instability of equilibria in dimension three %J Annales de l'Institut Fourier %D 1998 %P 1345-1357 %V 48 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1657/ %R 10.5802/aif.1657 %G en %F AIF_1998__48_5_1345_0
Brunella, Marco. Instability of equilibria in dimension three. Annales de l'Institut Fourier, Volume 48 (1998) no. 5, pp. 1345-1357. doi : 10.5802/aif.1657. https://aif.centre-mersenne.org/articles/10.5802/aif.1657/
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