The Poincaré-Bendixson theorem and arational foliations on the sphere
Nikolaev, Igor
Annales de l'Institut Fourier, Tome 46 (1996), p. 1159-1181 / Harvested from Numdam
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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.

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.

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     author = {Nikolaev, Igor},
     title = {The Poincar\'e-Bendixson theorem and arational foliations on the sphere},
     journal = {Annales de l'Institut Fourier},
     volume = {46},
     year = {1996},
     pages = {1159-1181},
     doi = {10.5802/aif.1544},
     mrnumber = {97h:58128},
     zbl = {0853.57027},
     mrnumber = {1415961},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1996__46_4_1159_0}
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Nikolaev, Igor. The Poincaré-Bendixson theorem and arational foliations on the sphere. Annales de l'Institut Fourier, Tome 46 (1996) pp. 1159-1181. doi : 10.5802/aif.1544. http://gdmltest.u-ga.fr/item/AIF_1996__46_4_1159_0/

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