Hamenstädt, Ursula Time-preserving conjugacies of geodesic flows. (English) Zbl 0766.58045 Ergodic Theory Dyn. Syst. 12, No. 1, 67-74 (1992). 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. Reviewer: C.S.Sharma (London) Cited in 1 ReviewCited in 10 Documents 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 Keywords:probability measure; ergodic theory; Hausdorff dimension; geodesic flows PDFBibTeX XMLCite \textit{U. Hamenstädt}, Ergodic Theory Dyn. Syst. 12, No. 1, 67--74 (1992; Zbl 0766.58045) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.