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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sambarino, A. 2016. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds. Mathematische Annalen, Vol. 364, Issue. 1-2, p. 453.


    Dankwart, Klaus 2014. Rigidity of flat surfaces under the boundary measure. Israel Journal of Mathematics, Vol. 199, Issue. 2, p. 623.


    Fanaï, Hamid-Reza 2005. Conjugaison Géodésique en rang 1. Bulletin of the Australian Mathematical Society, Vol. 71, Issue. 01, p. 121.


    Knieper, Gerhard 2002.


    Besson, G. Courtois, G. and Gallot, S. 1995. Entropies et rigidités des espaces localement symétriques de courbure strictement négative. Geometric and Functional Analysis, Vol. 5, Issue. 5, p. 731.


    Cao, Jianguo 1995. Rigidity for non-compact surfaces of finite area and certain Kähler manifolds. Ergodic Theory and Dynamical Systems, Vol. 15, Issue. 03,


    Hamenstädt, Ursula 1994. Regularity at infinity of compact negatively curved manifolds. Ergodic Theory and Dynamical Systems, Vol. 14, Issue. 03,


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Time-preserving conjugacies of geodesic flows

  • Ursula Hamenstädt (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700006581
  • Published online: 01 September 2008
Abstract
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.

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[B]F. Bonahon . Bouts des variétés hyperboliques de dimension 3. Ann. Math. 124 (1986), 71158.

[Bw]R. Bowen . Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972), 130.

[C]C. Croke . Rigidity for surfaces of non-positive curvature. Commun. Math. Helv. 65 (1989), 150169.

[H2]U. Hamenstädt . Entropy rigidity of locally symmetric spaces of negative curvature. Ann. Math. 131 (1990), 3551.

[K1]A. Katok . Entropy and closed geodesies. Ergod. Th. & Dynam. Sys. 2 (1982), 339367.

[L-Y]F. Ledrappier & L.-S. Young . The metric entropy of diffeomorphisms I, II. Ann. Math. 122 (1985), 509574.

[L]F. Ledrappier . Harmonic measure and Bowen-Margulis measure. Israel J. Math. 71 (1990), 275–187.

[O]J. P. Otal . Le spectre marqué des longeurs des surfaces à courbure negative. Ann. Math. 131 (1990), 151162.

[S]D. Sullivan . Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math. 36 (1976), 225255.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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