First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
Anatole Katok; Ralph J. Spatzier
Publications Mathématiques de l'IHÉS (1994)
- Volume: 79, page 131-156
- ISSN: 0073-8301
Access Full Article
topHow to cite
topKatok, Anatole, and Spatzier, Ralph J.. "First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity." Publications Mathématiques de l'IHÉS 79 (1994): 131-156. <http://eudml.org/doc/104094>.
@article{Katok1994,
author = {Katok, Anatole, Spatzier, Ralph J.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {-action; -action; Anosov actions; rigidity},
language = {eng},
pages = {131-156},
publisher = {Institut des Hautes Études Scientifiques},
title = {First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity},
url = {http://eudml.org/doc/104094},
volume = {79},
year = {1994},
}
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
PB - Institut des Hautes Études Scientifiques
VL - 79
SP - 131
EP - 156
LA - eng
KW - -action; -action; Anosov actions; rigidity
UR - http://eudml.org/doc/104094
ER -
References
top- [1] W. CASSELMAN and D. MILIČIČ, Asymptotic behavior of matrix coefficients of admissible representations, Duke J. of Math., 49 (1982), 869-930. Zbl0524.22014MR85a:22024
- [2] M. COWLING, Sur les coefficients des représentations unitaires des groupes de Lie simple, Lecture Notes in Mathematics, 739, 1979, 132-178, Springer Verlag. Zbl0417.22010MR81e:22019
- [3] Harish CHANDRA, Spherical functions on a semisimple Lie group, I, Amer J. of Math., 80 (1958), 241-310. Zbl0093.12801MR20 #925
- [4] M. HIRSCH, C. PUGH and M. SHUB, Invariant manifolds, Lecture Notes in Mathematics, 583, Springer Verlag, Berlin, 1977. Zbl0355.58009MR58 #18595
- [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. Zbl0725.58034MR92b:58179
- [7] H.-C. IMHOF, An Anosov action on the bundle of Weyl chambers, Ergod. Th. and Dyn. Syst., 5 (1985), 587-599. Zbl0555.58023MR87g:58103
- [8] J.-L. JOURNÉ, On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. Zbl0603.58019MR88b:58103
- [9] J.-L. JOURNÉ, A regularity lemma for functions of several variables, Revista Math. Iber., 4 (2), (1988), 187-193. Zbl0699.58008MR91j:58123
- [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. Zbl0836.57026MR95b:35042
- [11] A. KATOK and R. J. SPATZIER, Differential rigidity of Anosov actions of higher rank Abelian groups, in preparation. Zbl0938.37010
- [12] A. KATOK and R. J. SPATZIER, Differential rigidity of projective lattice actions, in preparation. Zbl0938.37010
- [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. Zbl0273.58013
- [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. Zbl0603.58016MR88h:58091
- [16] G. A. MARGULIS, Discrete subgroups of semisimple Lie groups, Springer Verlag, Berlin, 1991. Zbl0732.22008MR92h:22021
- [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. Zbl0625.58023MR89d:58102
- [18] C. PUGH and M. SHUB, Ergodicity of Anosov actions, Inventiones Math., 15 (1972), 1-23. Zbl0236.58007MR45 #4456
- [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. Zbl0254.22005MR58 #22394a
- [21] M. RATNER, The rate of mixing for geodesic and horocycle flows, Ergod. Th. and Dyn. Syst., 7 (1987), 267-288. Zbl0623.22008MR88j:58103
- [22] G. WARNER, Harmonic Analysis on semisimple Lie groups I, Springer Verlag, Berlin, 1972. Zbl0265.22020
- [23] R. J. ZIMMER, Ergodic theory and semisimple groups, Boston, Birkhäuser, 1984. Zbl0571.58015MR86j:22014
Citations in EuDML Documents
top- Stéphane Le Borgne, Françoise Pène, Vitesse dans le théorème limite central pour certains systèmes dynamiques quasi-hyperboliques
- Sergiy Maksymenko, ∞-jets of diffeomorphisms preserving orbits of vector fields
- Alejandro Kocsard, Cohomologically rigid vector fields : the Katok conjecture in dimension 3
- Stéphane Le Borgne, Principes d'invariance pour les flots diagonaux sur SL(d,R)/SL(d,Z)
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.