Measure preserving pseudo-groups and a theorem of Sacksteder
Annales de l'Institut Fourier, Tome 25 (1975) no. 1, pp. 237-249.

Ce travail est fondé sur un théorème de Sacksteder qui généralise un résultat classique de Denjoy. En utilisant ce théorème et quelques résultats sur l’existence d’une mesure invariante, on déduit des résultats relatifs aux ensembles minimaux pour les groupes de difféomorphismes du cercle et pour les feuilletages de codimension un.

This note is based on a theorem of Sacksteder which generalizes a classical result of Denjoy. Using this theorem and results on the existence of invariant measures, new results are obtained concerning minimal sets for groups of diffeomorphisms of the circle and for foliations of codimension one.

@article{AIF_1975__25_1_237_0,
     author = {Plante, Joseph F.},
     title = {Measure preserving pseudo-groups and a theorem of {Sacksteder}},
     journal = {Annales de l'Institut Fourier},
     pages = {237--249},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     number = {1},
     year = {1975},
     doi = {10.5802/aif.550},
     mrnumber = {51 #14100},
     zbl = {0299.58007},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.550/}
}
TY  - JOUR
AU  - Plante, Joseph F.
TI  - Measure preserving pseudo-groups and a theorem of Sacksteder
JO  - Annales de l'Institut Fourier
PY  - 1975
SP  - 237
EP  - 249
VL  - 25
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.550/
DO  - 10.5802/aif.550
LA  - en
ID  - AIF_1975__25_1_237_0
ER  - 
%0 Journal Article
%A Plante, Joseph F.
%T Measure preserving pseudo-groups and a theorem of Sacksteder
%J Annales de l'Institut Fourier
%D 1975
%P 237-249
%V 25
%N 1
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.550/
%R 10.5802/aif.550
%G en
%F AIF_1975__25_1_237_0
Plante, Joseph F. Measure preserving pseudo-groups and a theorem of Sacksteder. Annales de l'Institut Fourier, Tome 25 (1975) no. 1, pp. 237-249. doi : 10.5802/aif.550. http://www.numdam.org/articles/10.5802/aif.550/

[1] F. Greenleaf, Invariant means on topological groups, Van Nostrand, New York (1969). | MR | Zbl

[2] M. Hirsch, W. Thurston, Foliated bundles, flat manifolds and invariant measures, Annals of Math., (to appear). | Zbl

[3] R. Moussu, F. Pelletier, Sur le théorème de Poincaré-Bendixson, Annales de l'Institut Fourier, 24 (1974), 131-148. | Numdam | MR | Zbl

[4] V. Nemytskii, V. Stepanov, Qualitative theory of differential equations, Princeton University Press (1960). | MR | Zbl

[5] J. Plante, A generalization of the Poincaré-Bendixson theorem for foliations of codimension one, Topology, 12 (1973), 177-181. | MR | Zbl

[6] J. Plante, On the existence of exceptional minimal sets in foliations of codimension one, J. Differential Equations, 15 (1974), 178-194. | MR | Zbl

[7] R. Sacksteder, Foliations and pseudgroups, American J. of Math., 87 (1965), 79-102. | MR | Zbl

[8] R. Sacksteder, Groups and pseudogroups acting on S1 and R1, Mimeograph notes, Columbia University.

[9] J. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry, 2 (1968), 421-446. | MR | Zbl

Cité par Sources :