Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-30T23:42:03.474Z Has data issue: false hasContentIssue false

Regularity of time-preserving conjugacies for contact Anosov flows with C1-Anosov splitting

Published online by Cambridge University Press:  19 September 2008

Ursula Hamenstädt
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstrasse 1, 5300 Bonn, Germany

Abstract

Let (resp. ) be a smooth contact flow on a compact manifold V1 (resp.) V2 with Anosov splitting of class C1. We show that every time-preserving conjugacy Λ:(V1, )→( V2, ) is necessarily of class C2.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[C1]Croke, C.. Rigidity for surfaces of non-positive curvature. Comment. Math. Helv. 65 (1989), 150169.CrossRefGoogle Scholar
[C2]Croke, C.. Rigidity and the distance between boundary points. J. Diff. Geom. 33 (1991), 445464.Google Scholar
[C-F-F]Croke, C., Fathi, A. & Feldman, J.. The marked length spectrum of a surface of non-positive curvature. Preprint.Google Scholar
[F-O]Feldman, J. & Ornstein, D.. Semi-rigidity of horocycle flows over surfaces of variable negative curvature. Ergod. Th. & Dynam. Sys. 7 (1987), 4972.CrossRefGoogle Scholar
[H]Hamenstädt, U.. Time preserving conjugacies of geodesic flows. Ergod. Th. & Dynam. Svs. 12 (1992), 6774.CrossRefGoogle Scholar
[H-P]Hirsch, M. & Pugh, C.. Smoothness of horocycle foliations. J. Diff. Geom. (1975), 225238.Google Scholar
[Kn1]Kanai, M.. Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations. Ergod. Th. & Dynam. Sys. 8 (1988), 215239.CrossRefGoogle Scholar
[Kn2]Kanai, M.. Differential geometric studies on dynamics of geodesic and frame flows. Preprint.CrossRefGoogle Scholar
[K1]Katok, A.. Entropy and closed geodesies. Ergod. Th. & Dynam. Sys. 2 (1982), 339367.CrossRefGoogle Scholar
[K2]Katok, A.. Four applications of conformal equivalence to geometry and dynamics. Ergod. Th. & Dynam. Sys. 8 (1988), 139152.Google Scholar
[K-N]Kobayashi, S. & Nomizu, K.. Foundations of Differential Geometry I. Interscience, New York, 1963.Google Scholar
[M]Mañé, R.. Ergodic theory and differentiable dynamics. Ergebnisse der Mathematik III. Band 8, Springer, Berlin, 1987.Google Scholar
[O1]Otal, J. P.. Le spectre marqué des longeurs des surfaces à courbure négative. Ann. Math. 131 (1990), 151162.CrossRefGoogle Scholar
[O2]Otal, J. P.. Sur les longeurs des géodésiques d'une métrique à courbure négative dans le disque. Comment. Math. Helv. 65 (1990), 334347.CrossRefGoogle Scholar