Flots d’Anosov à distributions stable et instable différentiables
Journal of the American Mathematical Society, Tome 05 (1992) no. 1, pp. 33-74

Voir la notice de l'article provenant de la source American Mathematical Society

We describe which Anosov flows on compact manifolds have ${C^\infty }$ stable and unstable distributions and a contact canonical $1$-form: up to finite coverings and up to a ${C^\infty }$ change of parameters, each of them is isomorphic to the geodesic flow on (the unit tangent bundle of) a compact locally symmetric space of strictly negative curvature.
@article{10_1090_S0894_0347_1992_1124979_1,
     author = {Benoist, Yves and Foulon, Patrick and Labourie, Fran\~A{\textsection}ois},
     title = {Flots {d\^a€™Anosov} {\~A~} distributions stable et instable {diff\~A{\textcopyright}rentiables}},
     journal = {Journal of the American Mathematical Society},
     pages = {33--74},
     publisher = {mathdoc},
     volume = {05},
     number = {1},
     year = {1992},
     doi = {10.1090/S0894-0347-1992-1124979-1},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1992-1124979-1/}
}
TY  - JOUR
AU  - Benoist, Yves
AU  - Foulon, Patrick
AU  - Labourie, François
TI  - Flots d’Anosov à distributions stable et instable différentiables
JO  - Journal of the American Mathematical Society
PY  - 1992
SP  - 33
EP  - 74
VL  - 05
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1992-1124979-1/
DO  - 10.1090/S0894-0347-1992-1124979-1
ID  - 10_1090_S0894_0347_1992_1124979_1
ER  - 
%0 Journal Article
%A Benoist, Yves
%A Foulon, Patrick
%A Labourie, François
%T Flots d’Anosov à distributions stable et instable différentiables
%J Journal of the American Mathematical Society
%D 1992
%P 33-74
%V 05
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1992-1124979-1/
%R 10.1090/S0894-0347-1992-1124979-1
%F 10_1090_S0894_0347_1992_1124979_1
Benoist, Yves; Foulon, Patrick; Labourie, François. Flots d’Anosov à distributions stable et instable différentiables. Journal of the American Mathematical Society, Tome 05 (1992) no. 1, pp. 33-74. doi: 10.1090/S0894-0347-1992-1124979-1

[1] Anosov, D. V. Geodesic flows on closed Riemannian manifolds of negative curvature Trudy Mat. Inst. Steklov. 1967 209

[2] Benoist, Yves, Foulon, Patrick, Labourie, Franã§Ois Flots d’Anosov à distributions stable et instable différentiables C. R. Acad. Sci. Paris Sér. I Math. 1990 351 354

[3] Eberlein, P., O’Neill, B. Visibility manifolds Pacific J. Math. 1973 45 109

[4] Feres, Renato Geodesic flows on manifolds of negative curvature with smooth horospheric foliations Ergodic Theory Dynam. Systems 1991 653 686

[5] Feres, Renato, Katok, Anatole Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows Ergodic Theory Dynam. Systems 1989 427 432

[6] Feres, Renato, Katok, Anatole Anosov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature Ergodic Theory Dynam. Systems 1990 657 670

[7] Foulon, Patrick, Labourie, Franã§Ois Flots d’Anosov à distributions de Liapounov différentiables C. R. Acad. Sci. Paris Sér. I Math. 1989 255 260

[8] Ghys, ÉTienne Flots d’Anosov dont les feuilletages stables sont différentiables Ann. Sci. École Norm. Sup. (4) 1987 251 270

[9] Greub, Werner, Halperin, Stephen, Vanstone, Ray Connections, curvature, and cohomology 1976

[10] Gromov, Michael Rigid transformations groups 1988 65 139

[11] Hirsch, Morris W., Pugh, Charles C. Stable manifolds and hyperbolic sets 1970 133 163

[12] Hurder, S., Katok, A. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows Inst. Hautes Études Sci. Publ. Math. 1990

[13] Helgason, Sigurdur Differential geometry, Lie groups, and symmetric spaces 1978

[14] Kanai, Masahiko Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations Ergodic Theory Dynam. Systems 1988 215 239

[15] Kobayashi, Shoshichi, Nomizu, Katsumi Foundations of differential geometry. Vol I 1963

[16] Mostow, G. D. Intersections of discrete subgroups with Cartan subgroups J. Indian Math. Soc. 1970

[17] Raghunathan, M. S. Discrete subgroups of Lie groups 1972

[18] Satake, Ichirã´ Algebraic structures of symmetric domains 1980

Cité par Sources :