A Symbolic Proof of a Theorem of Margulis on Geodesic Arcs on Negatively Curved Manifolds

DOI10.2307/2374915zbMath0828.58025OpenAlexW2320252774MaRDI QIDQ4698283

Mark Pollicott

Publication date: 14 January 1996

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

Full work available at URL: https://doi.org/10.2307/2374915

zbMATH Keywords

geodesic flowtopological entropyhyperbolic flows

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Entropy and other invariants (28D20) Entropy in general topology (54C70) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Dynamical systems with hyperbolic behavior (37D99)

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Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature ⋮ Amenability, critical exponents of subgroups and growth of closed geodesics ⋮ Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs ⋮ On the Bose-Maslov statistics in the case of infinitely many degrees of freedom ⋮ Remark on the inverse abstract prime number theorem ⋮ On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators ⋮ Quantitative ergodic theorems and their number-theoretic applications ⋮ Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples

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