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Time-preserving conjugacies of geodesic flows. (English) Zbl 0766.58045

This is a study of certain Borel-probability measures invariant under the geodesic flow on the tangent bundle of a compact negatively curved manifold \(M\). By interpreting 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 \(M\), the author proves the necessary and sufficient condition for the existence of time-preserving conjugacies of the underlying geodesic flows.

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37A99 Ergodic theory
28A78 Hausdorff and packing measures
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References:

[1] Federer, Springer Grundlehren 153 pp none– (1969)
[2] Gromov, Three remarks on geodesic dynamics and fundamental group · Zbl 1002.53028
[3] DOI: 10.2307/2373590 · Zbl 0254.58005 · doi:10.2307/2373590
[4] DOI: 10.2307/1971388 · Zbl 0671.57008 · doi:10.2307/1971388
[5] DOI: 10.1007/BF01390011 · Zbl 0335.57015 · doi:10.1007/BF01390011
[6] DOI: 10.2307/1971511 · Zbl 0699.58018 · doi:10.2307/1971511
[7] Mostow, Ann. Math. Studies 78 (1973)
[8] DOI: 10.1007/BF02773746 · Zbl 0728.53029 · doi:10.1007/BF02773746
[9] DOI: 10.2307/1971328 · Zbl 0605.58028 · doi:10.2307/1971328
[10] Katok, Ergod. Th. & Dynam. Sys. 2 pp 339– (1982)
[11] Katik, Ergod. Th. & Dynam. Sys. 8 pp 139– (1988)
[12] Hamenstädt, J. Diff. Geom. 34 pp 193– (1991)
[13] DOI: 10.2307/1971507 · Zbl 0699.53049 · doi:10.2307/1971507
[14] Hamenstädt, Ergod. Th. & Dynam. Sys. 9 pp 455– (1989)
[15] DOI: 10.1007/BF02566599 · Zbl 0704.53035 · doi:10.1007/BF02566599
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