Limit sets of foliations
Sacksteder, Richard ; Schwartz, Art J.
Annales de l'Institut Fourier, Tome 15 (1965), p. 201-213 / Harvested from Numdam
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Soit V une variété munie d’une structure feuilletée de co-dimension un. On démontre plusieurs théorème relatifs à des conditions entraînant que le groupe d’holonomie et le pseudo-groupe d’holonomie d’une certaine feuille F⊂V est infini.

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     author = {Sacksteder, Richard and Schwartz, Art J.},
     title = {Limit sets of foliations},
     journal = {Annales de l'Institut Fourier},
     volume = {15},
     year = {1965},
     pages = {201-213},
     doi = {10.5802/aif.213},
     mrnumber = {32 \#6489},
     zbl = {0136.20904},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1965__15_2_201_0}
}

Sacksteder, Richard; Schwartz, Art J. Limit sets of foliations. Annales de l'Institut Fourier, Tome 15 (1965) pp. 201-213. doi : 10.5802/aif.213. http://gdmltest.u-ga.fr/item/AIF_1965__15_2_201_0/

[1] F. Haas, On the global behavior of differential equations on two-dimensional manifolds, Proceedings of the American Mathematical Society, vol. 4 (1953), 630-636. | Zbl 0051.32404

[2] F. Haas, Poincaré-Bendix type theorems for two-dimensional manifolds different from the torus, Annals of Mathematics, vol. 59 (1953), 292-299. | Zbl 0057.06902

[3] A. Haefliger, Variétés feuilletées, Annali della Scuola Normale Superiore di Pisa, III, vol. CVI (1962), 367-397. | Numdam | Zbl 0122.40702

[4] H. Kneser, Regulare Kurvenscharen auf den Ringenflächen, Mathematische Annalen, vol. 91 (1924), 135-154. | JFM 50.0371.03

[5] V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press (1960). | Zbl 0089.29502

[6] G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Scientifiques et Industrielles, Hermann, Paris (1952). | Zbl 0049.12602

[7] R. Sacksteder, Foliations and pseudogroups, The American Journal of Mathematics, vol. 87 (1965), 79-102. | Zbl 0136.20903

[8] A. J. Schwartz, A generalization of the Poincare-Bendixson theorem to closed two-dimensional manifolds, The American Journal of Mathematics, vol. 85 (1963), 453-458. | Zbl 0116.06803