The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 4, page 1159-1181
  • ISSN: 0373-0956

Abstract

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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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Nikolaev, Igor. "The Poincaré-Bendixson theorem and arational foliations on the sphere." Annales de l'institut Fourier 46.4 (1996): 1159-1181. <http://eudml.org/doc/75203>.

@article{Nikolaev1996,
abstract = {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.},
author = {Nikolaev, Igor},
journal = {Annales de l'institut Fourier},
keywords = {foliation; two-dimensional manifold; singular point; invariant measure},
language = {eng},
number = {4},
pages = {1159-1181},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Poincaré-Bendixson theorem and arational foliations on the sphere},
url = {http://eudml.org/doc/75203},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Nikolaev, Igor
TI - The Poincaré-Bendixson theorem and arational foliations on the sphere
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 4
SP - 1159
EP - 1181
AB - 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.
LA - eng
KW - foliation; two-dimensional manifold; singular point; invariant measure
UR - http://eudml.org/doc/75203
ER -

References

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