Harmonic measures and Bowen-Margulis measures

DOI10.1007/BF02773746zbMath0728.53029MaRDI QIDQ804966

François Ledrappier

Publication date: 1990

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Brownian motiongeodesic flowmean curvatureLaplaciantopological entropynegative curvatureBorel measuresabsoluteKaimanovich entropy

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Global Riemannian geometry, including pinching (53C20) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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Cites Work

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• The Dirichlet problem at infinity for a negatively curved manifold
• Positive harmonic functions on complete manifolds of negative curvature
• Unique ergodicity for horocycle foliations
• Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• Homology properties of Y-systems
• Certain measures associated with U-flows on compact manifolds
• A new description of the Bowen—Margulis measure
• Four applications of conformal equivalence to geometry and dynamics
• Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms