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.
@article{AIF_1987__37_2_151_0, author = {Cano, Felipe}, title = {Final forms for a three-dimensional vector field under blowing-up}, journal = {Annales de l'Institut Fourier}, pages = {151--193}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {2}, year = {1987}, doi = {10.5802/aif.1091}, mrnumber = {88j:58105}, zbl = {0607.58027}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1091/} }
TY - JOUR AU - Cano, Felipe TI - Final forms for a three-dimensional vector field under blowing-up JO - Annales de l'Institut Fourier PY - 1987 SP - 151 EP - 193 VL - 37 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1091/ DO - 10.5802/aif.1091 LA - en ID - AIF_1987__37_2_151_0 ER -
%0 Journal Article %A Cano, Felipe %T Final forms for a three-dimensional vector field under blowing-up %J Annales de l'Institut Fourier %D 1987 %P 151-193 %V 37 %N 2 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1091/ %R 10.5802/aif.1091 %G en %F AIF_1987__37_2_151_0
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://www.numdam.org/articles/10.5802/aif.1091/
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