Stable ergodicity of skew products

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 32, Issue 6, 1999, Pages 859-889

  Burns, Keith ^a   Wilkinson, Amie ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033472563     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(00)87721-6     Document Type: Article

References (26)

1. [AKS] R. Adler, B. Kitchens and M. Shub, Stably ergodic skew products, Discrete and Continuous Dynamical Systems, Vol. 2, 1996, pp. 349-350.
2. [B1] M. Brin, Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature, Func. Anal. Appl., Vol. 9, 1975, no. 1, pp. 9-19.
3. [B2] M. Brin, The topology of group extensions of C systems, Mat. Zametki, Vol. 18, 1975, no. 3, pp. 453-465.
4. [BP] M. Brin and Ja. Pesin, Partially hyperbolic dynamical systems, Math. USSR Izvestija, Vol. 8, 1974, no. 1, pp. 177-218.
5. [BPW] K. Burns, C. Pugh and A. Wilkinson, Stable ergodicity and Anosov flows, to appear in Topology.
6. [CE] J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North Holland/American Elsevier, 1975.
7. [FP] M. Field and W. Parry, Stable ergodicity of skew extensions by compact Lie groups, Topology, Vol. 38, 1999, No 1, pp. 167-187.
8. [GPS] M. Grayson, C. Pugh and M. Shub, Stably ergodic diffeomorphisms, Ann. Math., Vol. 140, 1994, pp. 295-329.
9. [H] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978.
10. [HPS] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, 1977.
11. [Hu] S.-T. Hu, Homotopy Theory, Academic Press, 1959.
12. [Hum] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer Verlag, 1972.
13. [J] J.-L. Journé, A regularity lemma for functions of several variables, Rev. Mat. Iberoamericana, Vol. 4, 1988, no. 2, pp. 187-193.
14. [KK] A. Katok and A. Kononenko, Cocycles' stability for partially hyperbolic systems, Math. Res. Lett., Vol. 3, 1996, no. 2, pp. 191-210.
15. [Ma1] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., Vol. 96, 1974, pp. 422-429.
16. [Ma2] A. Manning, Anosov diffeomorphisms on nilmanifolds, Proc. Amer. Math. Soc., Vol. 38, 1973, pp. 423-426.
17. [Mi] J. Milnor, Morse Theory, Princeton University Press, 1969.
18. [N] K. Nomizu, Lie Groups and Differential Geometry, Mathematical Society of Japan, 1956.
19. [P] W. Parry, Entropy and Generators in Ergodic Theory, W. A. Benjamin, Inc. 1969.
20. [PP] W. Parry and M. Pollicott, Stability of mixing for toral extensions of hyperbolic systems, Tr. Mat. Inst. Steklova, Vol. 216, 1997, Din. Sist. i Smezhnye Vopr., pp. 354-363.
21. [PS1] C. Pugh and M. Shub, Stably ergodic dynamical systems and partial hyperbolicity, J. of Complexity, Vol. 13, 1997, pp. 125-179.
22. [PS2] C. Pugh and M. Shub, Stable Ergodicity and Julienne Quasiconformality, September, 1997 preprint.
23. [R] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, J. Analyse Math., Vol. 34, 1978, pp. 36-60.
24. [Wa] C. Walkden, Stable Ergodic Properties of Cocycles over Hyperbolic Attractors, 1997 preprint.
25. [Wi] A. Wilkinson, Stable ergodicity of the time one map of a geodesic flow, Ergod. Th. and Dynam. Syst., Vol. 18, 1998, no. 6, pp. 1545-1588.
26. [Y] H. Yamabe, On an arcwise connected subgroup of a Lie group, Osaka Math. J., Vol. 2, 1950, pp. 13-14.