The Poincaré-Bendixson theorem and arational foliations on the sphere
Annales de l'Institut Fourier, Volume 46 (1996) no. 4, p. 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.
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {4},
     year = {1996},
     pages = {1159-1181},
     doi = {10.5802/aif.1544},
     mrnumber = {1415961},
     zbl = {0853.57027},
     mrnumber = {97h:58128},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIF_1996__46_4_1159_0/

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