The Poincaré-Bendixson theorem and arational foliations on the sphere
Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 1159-1181.

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.

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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://www.numdam.org/articles/10.5802/aif.1544/

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