Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Vadim A. Kaimanovich (1990)
Annales de l'I.H.P. Physique théorique
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Vadim A. Kaimanovich (1990)
Annales de l'I.H.P. Physique théorique
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Yves Coudène, Barbara Schapira (2014)
Journal de l’École polytechnique — Mathématiques
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We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by trajectories not bounding a flat strip. This is done by showing that Dirac measures on periodic orbits are dense in that set. In the case of a compact surface, we...
Manuel Stadlbauer (2004)
Fundamenta Mathematicae
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For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the...
Hämenstadt, Ursula (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Francis Bonahon (1997)
Annales scientifiques de l'École Normale Supérieure
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Marco Brunella (1994)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Matveev, Vladimir S., Topalov, Petar J. (2000)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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McShane, Greg (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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