Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.
Nous considérons les feuilletages de la 2-sphère avec un nombre fini de singularités non-orientables. Nous établissons un théorème de type Poincaré-Bendixson. En particulier, nous résolvons un problème de H. Rosenberg concernant les labyrinthes.
@article{AIF_1996__46_4_1159_0, author = {Nikolaev, Igor}, title = {The {Poincar\'e-Bendixson} theorem and arational foliations on the sphere}, journal = {Annales de l'Institut Fourier}, pages = {1159--1181}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {4}, year = {1996}, doi = {10.5802/aif.1544}, zbl = {0853.57027}, mrnumber = {1415961}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1544/} }
TY - JOUR AU - Nikolaev, Igor TI - The Poincaré-Bendixson theorem and arational foliations on the sphere JO - Annales de l'Institut Fourier PY - 1996 SP - 1159 EP - 1181 VL - 46 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1544/ DO - 10.5802/aif.1544 LA - en ID - AIF_1996__46_4_1159_0 ER -
%0 Journal Article %A Nikolaev, Igor %T The Poincaré-Bendixson theorem and arational foliations on the sphere %J Annales de l'Institut Fourier %D 1996 %P 1159-1181 %V 46 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1544/ %R 10.5802/aif.1544 %G en %F AIF_1996__46_4_1159_0
Nikolaev, Igor. The Poincaré-Bendixson theorem and arational foliations on the sphere. Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 1159-1181. doi : 10.5802/aif.1544. http://archive.numdam.org/articles/10.5802/aif.1544/
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