Volume 15, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Totally nonsymplectic Anosov actions on tori and nilmanifolds

David Fisher, Boris Kalinin and Ralf Spatzier

Geometry & Topology 15 (2011) 191–216
Bibliography
1 L Auslander, L Green, F Hahn, Flows on homogeneous spaces, Annals of Math. Studies 53, Princeton Univ. Press (1963) MR0167569
2 L Barreira, Y B Pesin, Lyapunov exponents and smooth ergodic theory, Univ. Lecture Series 23, Amer. Math. Soc. (2002) MR1862379
3 R Bowen, B Marcus, Unique ergodicity for horocycle foliations, Israel J. Math. 26 (1977) 43 MR0451307
4 M Einsiedler, T Fisher, Differentiable rigidity for hyperbolic toral actions, Israel J. Math. 157 (2007) 347 MR2342454
5 D Fisher, G Margulis, Local rigidity of affine actions of higher rank groups and lattices, Ann. of Math. $(2)$ 170 (2009) 67 MR2521112
6 J Franks, Anosov diffeomorphisms on tori, Trans. Amer. Math. Soc. 145 (1969) 117 MR0253352
7 M Guysinsky, The theory of non-stationary normal forms, Ergodic Theory Dynam. Systems 22 (2002) 845 MR1908557
8 M Guysinsky, A Katok, Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations, Math. Res. Lett. 5 (1998) 149 MR1618331
9 M W Hirsch, C C Pugh, M Shub, Invariant manifolds, Lecture Notes in Math. 583, Springer (1977) MR0501173
10 S Hurder, Rigidity for Anosov actions of higher rank lattices, Ann. of Math. $(2)$ 135 (1992) 361 MR1154597
11 B Kalinin, A Katok, Invariant measures for actions of higher rank abelian groups, from: "Smooth ergodic theory and its applications (Seattle, WA, 1999)" (editors A Katok, R de la Llave, Y Pesin, H Weiss), Proc. Sympos. Pure Math. 69, Amer. Math. Soc. (2001) 593 MR1858547
12 B Kalinin, A Katok, Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori, J. Mod. Dyn. 1 (2007) 123 MR2261075
13 B Kalinin, V Sadovskaya, Global rigidity for totally nonsymplectic Anosov $\mathbb Z^k$ actions, Geom. Topol. 10 (2006) 929 MR2240907
14 B Kalinin, V Sadovskaya, On the classification of resonance-free Anosov $\mathbb Z^k$ actions, Michigan Math. J. 55 (2007) 651 MR2372620
15 B Kalinin, R Spatzier, On the classification of Cartan actions, Geom. Funct. Anal. 17 (2007) 468 MR2322492
16 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, Encyc. of Math. and its Appl. 54, Cambridge Univ. Press (1995) MR1326374
17 A Katok, J Lewis, Local rigidity for certain groups of toral automorphisms, Israel J. Math. 75 (1991) 203 MR1164591
18 A Katok, R Spatzier, First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity, Inst. Hautes Études Sci. Publ. Math. (1994) 131 MR1307298
19 A Katok, R Spatzier, Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions, Tr. Mat. Inst. Steklova 216 (1997) 292 MR1632177
20 R de la Llave, J M Marco, R Moriyón, Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation, Ann. of Math. $(2)$ 123 (1986) 537 MR840722
21 A Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math. 96 (1974) 422 MR0358865
22 G A Margulis, N Qian, Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices, Ergodic Theory Dynam. Systems 21 (2001) 121 MR1826664
23 D Montgomery, L Zippin, Topological transformation groups, Robert E Krieger Publishing (1974) MR0379739
24 N T Qian, Anosov automorphisms for nilmanifolds and rigidity of group actions, Ergodic Theory Dynam. Systems 15 (1995) 341 MR1332408
25 F Rodriguez Hertz, Global rigidity of certain abelian actions by toral automorphisms, J. Mod. Dyn. 1 (2007) 425 MR2318497
26 S J Schreiber, On growth rates of subadditive functions for semiflows, J. Differential Equations 148 (1998) 334 MR1643183
27 P Walters, Conjugacy properties of affine transformations of nilmanifolds, Math. Systems Theory 4 (1970) 327 MR0414830