The central limit theorem for the geodesic flow on noncompact manifolds of constant negative curvature

DOI10.1215/S0012-7094-94-07408-5zbMath0809.58031MaRDI QIDQ1331692

Yves Le Jan

Publication date: 29 March 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

hyperbolic manifoldgeodesic flowcentral limit theoremfunction average

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Diffusion processes and stochastic analysis on manifolds (58J65) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (11)

Asymptotic windings of horocycles ⋮ Vitesse dans le théorème limite central pour certains systèmes dynamiques quasi-hyperboliques ⋮ Free energy for Brownian and geodesic homology ⋮ Flexibility of statistical properties for smooth systems satisfying the central limit theorem ⋮ Central limit theorems for group actions which are exponentially mixing of all orders ⋮ Temporal distributional limit theorems for dynamical systems ⋮ Asymptotic windings over the trefoil knot ⋮ Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard ⋮ Central limit theorem and cohomological equation on homogeneous spaces ⋮ Asymptotic Counting in Conformal Dynamical Systems ⋮ Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Cites Work

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• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov. (Limit theorems for a class of Markov chains and applications to Anosov diffeomorphisms)
• The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
• Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions

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