First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
Publications Mathématiques de l'IHÉS, Tome 79 (1994), pp. 131-156. 
@article{PMIHES_1994__79__131_0,
     author = {Katok, Anatole and Spatzier, Ralph J.},
     title = {First cohomology of {Anosov} actions of higher rank abelian groups and applications to rigidity},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {131--156},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {79},
     year = {1994},
     mrnumber = {96c:58132},
     zbl = {0819.58027},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1994__79__131_0/}
}
TY  - JOUR
AU  - Katok, Anatole
AU  - Spatzier, Ralph J.
TI  - First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
JO  - Publications Mathématiques de l'IHÉS
PY  - 1994
SP  - 131
EP  - 156
VL  - 79
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1994__79__131_0/
LA  - en
ID  - PMIHES_1994__79__131_0
ER  - 
%0 Journal Article
%A Katok, Anatole
%A Spatzier, Ralph J.
%T First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
%J Publications Mathématiques de l'IHÉS
%D 1994
%P 131-156
%V 79
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1994__79__131_0/
%G en
%F PMIHES_1994__79__131_0
Katok, Anatole; Spatzier, Ralph J. First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Publications Mathématiques de l'IHÉS, Tome 79 (1994), pp. 131-156. http://www.numdam.org/item/PMIHES_1994__79__131_0/

[1] W. Casselman and D. Miličič, Asymptotic behavior of matrix coefficients of admissible representations, Duke J. of Math., 49 (1982), 869-930. | MR | Zbl

[2] M. Cowling, Sur les coefficients des représentations unitaires des groupes de Lie simple, Lecture Notes in Mathematics, 739, 1979, 132-178, Springer Verlag. | MR | Zbl

[3] Harish Chandra, Spherical functions on a semisimple Lie group, I, Amer J. of Math., 80 (1958), 241-310. | MR | Zbl

[4] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, 583, Springer Verlag, Berlin, 1977. | MR | Zbl

[5] R. Howe, A notion of rank for unitary representations of the classical groups, in A. FIGÀ TALAMANGA (ed.), Harmonic analysis and group representations, CIME, 1980.

[6] S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES, 72 (1990), 5-61. | Numdam | MR | Zbl

[7] H.-C. Imhof, An Anosov action on the bundle of Weyl chambers, Ergod. Th. and Dyn. Syst., 5 (1985), 587-599. | MR | Zbl

[8] J.-L. Journé, On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. | MR | Zbl

[9] J.-L. Journé, A regularity lemma for functions of several variables, Revista Math. Iber., 4 (2), (1988), 187-193. | MR | Zbl

[10] A. Katok and R. J. Spatzier, Cocycle rigidity of partially hyperbolic actions of higher rank abelian groups, Math. Res. Letters, 1 (1994), 193-202. | MR

[11] A. Katok and R. J. Spatzier, Differential rigidity of Anosov actions of higher rank Abelian groups, in preparation. | Zbl

[12] A. Katok and R. J. Spatzier, Differential rigidity of projective lattice actions, in preparation.

[13] A. Katok and R. J. Spatzier, Invariant measures for higher rank hyperbolic abelian actions, MSRI preprint, 059-92, Berkeley, 1992.

[14] A. Livshitz, Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. | Zbl

[15] R. De La Llavé, J. Marco and R. Moriyon, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math., 123 (1986), 537-611. | MR | Zbl

[16] G. A. Margulis, Discrete subgroups of semisimple Lie groups, Springer Verlag, Berlin, 1991. | MR | Zbl

[17] C. C. Moore, Exponential decay of correlation coefficients for geodesic flows, in C. C. MOORE (ed), Group representations, ergodic theory, operator algebras, and mathematical physics, Proceedings of a Conference in Honor of George Mackey, MSRI publications, Springer Verlag, 1987, 163-181. | MR | Zbl

[18] C. Pugh and M. Shub, Ergodicity of Anosov actions, Inventiones Math., 15 (1972), 1-23. | MR | Zbl

[19] N. Qian, Rigidity Phenomena of Group Actions on a Class of Nilmanifolds and Anosov Rn-Actions, Ph.D. thesis, California Institute of Technology, 1992.

[20] M. Raghunathan, Discrete subgroups of Lie groups, Springer Verlag, New York, 1972. | MR | Zbl

[21] M. Ratner, The rate of mixing for geodesic and horocycle flows, Ergod. Th. and Dyn. Syst., 7 (1987), 267-288. | MR | Zbl

[22] G. Warner, Harmonic Analysis on semisimple Lie groups I, Springer Verlag, Berlin, 1972. | Zbl

[23] R. J. Zimmer, Ergodic theory and semisimple groups, Boston, Birkhäuser, 1984. | MR | Zbl