previous :: next
Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
Viorel Niţicǎ and Andrei Török
Source: Duke Math. J. Volume 79, Number 3
(1995), 751-810.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285356
Mathematical Reviews number (MathSciNet): MR1355183
Zentralblatt MATH identifier: 0849.58049
Digital Object Identifier: doi:10.1215/S0012-7094-95-07920-4
References
[CEG] P. Collet, H. Epstein, and G. Gallavotti, Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties, Comm. Math. Phys. 95 (1984), no. 1, 61–112.
Mathematical Reviews (MathSciNet): MR85m:58143
Zentralblatt MATH: 0585.58022
Digital Object Identifier: doi:10.1007/BF01215756
Project Euclid: euclid.cmp/1103941454
[GK] V. Guillemin and D. Kazhdan, On the cohomology of certain dynamical systems, Topology 19 (1980), no. 3, 291–299.
Mathematical Reviews (MathSciNet): MR81j:58067
Zentralblatt MATH: 0498.58018
Digital Object Identifier: doi:10.1016/0040-9383(80)90014-2
[H1] S. Hurder, Rigidity for Anosov actions of higher rank lattices, Ann. of Math. (2) 135 (1992), no. 2, 361–410.
Mathematical Reviews (MathSciNet): MR93c:22018
Zentralblatt MATH: 0754.58029
Digital Object Identifier: doi:10.2307/2946593
[H2] S. Hurder, Infinitesimal rigidity of hyperbolic actions, preprint, 1993.
Mathematical Reviews (MathSciNet): MR1338481
Zentralblatt MATH: 0839.57027
Project Euclid: euclid.jdg/1214456480
[HPS] M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Math., vol. 583, Springer-Verlag, Berlin, 1977.
Mathematical Reviews (MathSciNet): MR58:18595
Zentralblatt MATH: 0355.58009
[J] J.-L. Journé, On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys. 106 (1986), no. 2, 345–351.
Mathematical Reviews (MathSciNet): MR88b:58103
Zentralblatt MATH: 0603.58019
Digital Object Identifier: doi:10.1007/BF01454979
Project Euclid: euclid.cmp/1104115704
[K] A. Katok, Dynamical systems with hyperbolic structure, Three Papers in Dynamical Systems, Amer. Math. Soc. Transl. Ser. 2, vol. 116, Amer. Math. Soc., Providence, 1981, pp. 43–95.
Zentralblatt MATH: 0598.58031
[KH] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, vol. 54, Cambridge Univ. Press, Cambridge, 1995.
Mathematical Reviews (MathSciNet): MR96c:58055
Zentralblatt MATH: 0878.58020
[KK] A. Katok and S. Katok, Higher cohomology for abelian groups of toral automorphisms, Ergodic Theory Dynam. Systems 15 (1995), no. 3, 569–592.
Mathematical Reviews (MathSciNet): MR96k:58167
Zentralblatt MATH: 0851.57039
Digital Object Identifier: doi:10.1017/S0143385700008531
[KL1] A. Katok and J. Lewis, Local rigidity for certain groups of toral automorphisms, Israel J. Math. 75 (1991), no. 2-3, 203–241.
Mathematical Reviews (MathSciNet): MR93g:58076
Zentralblatt MATH: 0785.22012
Digital Object Identifier: doi:10.1007/BF02776025
[KL2] A. Katok and J. Lewis, Global rigidity results for lattice actions on tori and new examples of volume-preserving actions, preprint, to appear in Israel J. Math., 1995.
Mathematical Reviews (MathSciNet): MR1380646
Zentralblatt MATH: 0857.57038
Digital Object Identifier: doi:10.1007/BF02761106
[KLZ] A. Katok, J. Lewis, and R. Zimmer, Cocycle superrigidity and rigidity for lattice actions on tori, preprint, 1992.
Mathematical Reviews (MathSciNet): MR1367273
Digital Object Identifier: doi:10.1016/0040-9383(95)00012-7
[KS] A. Katok and R. Spatzier, Differentiable rigidity of hyperbolic abelian actions, preprint, 1992.
[L1] A. Livsic, Homology properties of $U$ systems, Math. Notes 10 (1971), 758–763.
[L2] A. Livsic, Cohomology of dynamical systems, Math. U.S.S.R.-Izv. 6 (1972), 1278–1301.
Mathematical Reviews (MathSciNet): MR334287
[LS] A. Livsic and J. Sinai, On invariant measures compatible with the smooth structures for transitive $U$ systems, Soviet Math. Dokl. 13 (1972), 1656–1659.
[Lla] R. De La Llave, Analytic regularity of solutions of Livsic's cohomology equations and some applications to analytic conjugacy of hyperbolic dynamical systems, preprint, 1989.
[LMM] R. de la Llave, J. M. Marco, and R. Moriyon, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math. (2) 123 (1986), no. 3, 537–611.
Mathematical Reviews (MathSciNet): MR88h:58091
Zentralblatt MATH: 0603.58016
Digital Object Identifier: doi:10.2307/1971334
JSTOR: links.jstor.org
[M] G. A. Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 17, Springer-Verlag, Berlin, 1991.
Mathematical Reviews (MathSciNet): MR92h:22021
Zentralblatt MATH: 0732.22008
[NT] V. Niţică and A. Török, Regularity results for the solution of Livsic cohomology equation with values in diffeomorphism groups, to appear in Ergodic Theory Dynamical Systems.
Mathematical Reviews (MathSciNet): MR1389627
Zentralblatt MATH: 0892.58059
[PR] G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semisimple groups, Ann. of Math. (2) 96 (1972), 296–317.
Mathematical Reviews (MathSciNet): MR46:1965
Zentralblatt MATH: 0245.22013
Digital Object Identifier: doi:10.2307/1970790
JSTOR: links.jstor.org
[Q1] N. Qian, Local rigidity of Anosov actions on tori, preprint, 1993.
[Q2] N. T. Qian, Topological deformation rigidity of higher rank lattice actions, Math. Res. Lett. 1 (1994), no. 4, 485–499.
Mathematical Reviews (MathSciNet): MR95i:58144
Zentralblatt MATH: 0836.22016
[R] W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, New York, 1976.
Mathematical Reviews (MathSciNet): MR52:5893
Zentralblatt MATH: 0346.26002
[S1] D. Stowe, The stationary set of a group action, Proc. Amer. Math. Soc. 79 (1980), no. 1, 139–146.
Mathematical Reviews (MathSciNet): MR81b:57035
Zentralblatt MATH: 0454.57027
Digital Object Identifier: doi:10.2307/2042403
[S2] D. Stowe, Stable orbits of differentiable group actions, Trans. Amer. Math. Soc. 277 (1983), no. 2, 665–684.
Mathematical Reviews (MathSciNet): MR85c:57045
Zentralblatt MATH: 0523.57028
Digital Object Identifier: doi:10.2307/1999230
JSTOR: links.jstor.org
[Z1] R. J. Zimmer, Actions of semisimple groups and discrete subgroups, Proceedings of The International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, 1987, pp. 1247–1258.
Mathematical Reviews (MathSciNet): MR89j:22024
Zentralblatt MATH: 0671.57028
[Z2] R. Zimmer, Lattices in semisimple groups and invariant geometric structures on compact manifolds, Discrete Groups in Geometry and Analysis (New Haven, Conn., 1984), Progr. Math., vol. 67, Birkhäuser, Boston, 1987, pp. 152–210.
Mathematical Reviews (MathSciNet): MR88i:22025
Zentralblatt MATH: 0663.22008
[Z3] R. Zimmer, Infinitesimal rigidity for smooth actions of discrete subgroups of Lie groups, J. Differential Geom. 31 (1990), no. 2, 301–322.
Mathematical Reviews (MathSciNet): MR91f:22020
Zentralblatt MATH: 0696.57022
Project Euclid: euclid.jdg/1214444314
[Z4] R. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics, vol. 81, Birkhauser, Boston, 1984.
Mathematical Reviews (MathSciNet): MR86j:22014
Zentralblatt MATH: 0571.58015
previous :: next
Duke Mathematical Journal
