Final forms for a three-dimensional vector field under blowing-up
Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 151-193.

We study the final situations which may be obtained for a singular vector field by permissible blowing-ups of the ambient space (in dimension three). These situations are preserved by permissible blowing-ups and its structure is simple from the view-point of the integral branches. Technically, we take a logarithmic approach, by marking in each step the exceptional divisor of the transformation.

On étudie les situations finales que l’on peut obtenir pour un champ de vecteurs singulier en éclatant l’espace ambiant avec des centres permis (en dimension trois). Ces situations sont préservées par des éclatements permis et elles ont une structure simple du point de vue des courbes intégrales. Techniquement, on adopte une vision logarithmique, en signalant dans chaque étape le diviseur exceptionnel de la transformation.

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     title = {Final forms for a three-dimensional vector field under blowing-up},
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Cano, Felipe. Final forms for a three-dimensional vector field under blowing-up. Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 151-193. doi : 10.5802/aif.1091. http://archive.numdam.org/articles/10.5802/aif.1091/

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