Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T05:30:27.534Z Has data issue: false hasContentIssue false
  • English
  • Français

Time-preserving conjugacies of geodesic flows

Published online by Cambridge University Press:  19 September 2008

Ursula Hamenstädt
Ursula Hamenstädt
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstraβe 1, 5300 Bonn, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note we study Borel-probability measures on the unit tangent bundle ofa compact negatively curved manifold M that are invariant under the geodesic flow. We interpret the entropy of such a measure as a Hausdorff dimension with respect to a natural family of distances on the ideal boundary of the universal covering of M. This in term yields necessary and sufficient conditions for the existence of time preserving conjugacies of geodesic flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 67 - 74
Copyright
Copyright © Cambridge University Press 1992

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

[B]Bonahon, F.. Bouts des variétés hyperboliques de dimension 3. Ann. Math. 124 (1986), 71–158.CrossRefGoogle Scholar
[Bw]Bowen, R.. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972), 1–30.CrossRefGoogle Scholar
[C]Croke, C.. Rigidity for surfaces of non-positive curvature. Commun. Math. Helv. 65 (1989), 150–169.CrossRefGoogle Scholar
[F]Federer, H.. Geometric measure theory. Springer Grundlehren 153 (1969).Google Scholar
[G]Gromov, M.. Three remarks on geodesic dynamics and fundamental group. Preprint.Google Scholar
[HI]Hamenstädt, U.. A new description of the Bowen-Margulis measure. Ergod. Th. & Dynam. Sys. 9 (1989), 455–464.CrossRefGoogle Scholar
[H2]Hamenstädt, U.. Entropy rigidity of locally symmetric spaces of negative curvature. Ann. Math. 131 (1990), 35–51.CrossRefGoogle Scholar
[H3]Hamenstädt, U.. A geometric characterization of negatively curved locally symmetric spaces. J. Diff. Geom. 34 (1991), 193–221.Google Scholar
[K1]Katok, A.. Entropy and closed geodesies. Ergod. Th. & Dynam. Sys. 2 (1982), 339–367.CrossRefGoogle Scholar
[K2]Katik, A.. Four applications of conformal equivalence to geometry and dynamics. Ergod. Th. & Dynam. Sys. 8* (1988), 139–152.Google Scholar
[L-Y]Ledrappier, F. & Young, L.-S.. The metric entropy of diffeomorphisms I, II. Ann. Math. 122 (1985), 509–574.CrossRefGoogle Scholar
[L]Ledrappier, F.. Harmonic measure and Bowen-Margulis measure. Israel J. Math. 71 (1990), 275–187.CrossRefGoogle Scholar
[M]Mostow, G. D.. Strong rigidity of locally symmetric spaces. Ann. Math. Studies 78, Princeton: Princeton University Press, 1973.Google Scholar
[O]Otal, J. P.. Le spectre marqué des longeurs des surfaces à courbure negative. Ann. Math. 131 (1990), 151–162.CrossRefGoogle Scholar
[S]Sullivan, D.. Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math. 36 (1976), 225–255.CrossRefGoogle Scholar