@article{PMIHES_1994__79__131_0,
author = {Katok, Anatole and Spatzier, Ralf},
title = {First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity},
journal = {Publications Math\'ematiques de l'IH\'ES},
volume = {80},
year = {1994},
pages = {131-156},
mrnumber = {96c:58132},
zbl = {0819.58027},
language = {en},
url = {http://dml.mathdoc.fr/item/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 80 (1994) pp. 131-156. http://gdmltest.u-ga.fr/item/PMIHES_1994__79__131_0/
[1] and , Asymptotic behavior of matrix coefficients of admissible representations, Duke J. of Math., 49 (1982), 869-930. | MR 85a:22024 | Zbl 0524.22014
[2] , Sur les coefficients des représentations unitaires des groupes de Lie simple, Lecture Notes in Mathematics, 739, 1979, 132-178, Springer Verlag. | MR 81e:22019 | Zbl 0417.22010
[3] , Spherical functions on a semisimple Lie group, I, Amer J. of Math., 80 (1958), 241-310. | MR 20 #925 | Zbl 0093.12801
[4] , and , Invariant manifolds, Lecture Notes in Mathematics, 583, Springer Verlag, Berlin, 1977. | MR 58 #18595 | Zbl 0355.58009
[5] , A notion of rank for unitary representations of the classical groups, in A. FIGÀ TALAMANGA (ed.), Harmonic analysis and group representations, CIME, 1980.
[6] and , Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES, 72 (1990), 5-61. | Numdam | MR 92b:58179 | Zbl 0725.58034
[7] , An Anosov action on the bundle of Weyl chambers, Ergod. Th. and Dyn. Syst., 5 (1985), 587-599. | MR 87g:58103 | Zbl 0555.58023
[8] , On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. | MR 88b:58103 | Zbl 0603.58019
[9] , A regularity lemma for functions of several variables, Revista Math. Iber., 4 (2), (1988), 187-193. | MR 91j:58123 | Zbl 0699.58008
[10] and , Cocycle rigidity of partially hyperbolic actions of higher rank abelian groups, Math. Res. Letters, 1 (1994), 193-202. | MR 95b:35042
[11] and , Differential rigidity of Anosov actions of higher rank Abelian groups, in preparation. | Zbl 0938.37010
[12] and , Differential rigidity of projective lattice actions, in preparation.
[13] and , Invariant measures for higher rank hyperbolic abelian actions, MSRI preprint, 059-92, Berkeley, 1992.
[14] , Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. | Zbl 0273.58013
[15] , and , Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math., 123 (1986), 537-611. | MR 88h:58091 | Zbl 0603.58016
[16] , Discrete subgroups of semisimple Lie groups, Springer Verlag, Berlin, 1991. | MR 92h:22021 | Zbl 0732.22008
[17] , 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 89d:58102 | Zbl 0625.58023
[18] and , Ergodicity of Anosov actions, Inventiones Math., 15 (1972), 1-23. | MR 45 #4456 | Zbl 0236.58007
[19] , Rigidity Phenomena of Group Actions on a Class of Nilmanifolds and Anosov Rn-Actions, Ph.D. thesis, California Institute of Technology, 1992.
[20] , Discrete subgroups of Lie groups, Springer Verlag, New York, 1972. | MR 58 #22394a | Zbl 0254.22005
[21] , The rate of mixing for geodesic and horocycle flows, Ergod. Th. and Dyn. Syst., 7 (1987), 267-288. | MR 88j:58103 | Zbl 0623.22008
[22] , Harmonic Analysis on semisimple Lie groups I, Springer Verlag, Berlin, 1972. | Zbl 0265.22020
[23] , Ergodic theory and semisimple groups, Boston, Birkhäuser, 1984. | MR 86j:22014 | Zbl 0571.58015