Horocycle flow on geometrically finite surfaces

DOI10.1215/S0012-7094-90-06129-0zbMath0723.58041WikidataQ105994744 ScholiaQ105994744MaRDI QIDQ756822

Marc Burger

Publication date: 1990

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

zbMATH Keywords

LaplacianRadon measureshorocycle flowunit tangent bundlePoincaré discextremal generatorfinite subspaces

Mathematics Subject Classification ID

Integration on manifolds; measures on manifolds (58C35) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Related Items (56)

On the distribution of orbits of geometrically finite hyperbolic groups on the boundary ⋮ Polynomial mixing for time-changes of unipotent flows ⋮ Invariant Radon measures for horocycle flows on Abelian covers ⋮ On the rate of equidistribution of expanding horospheres in finite-volume quotients of \(\mathrm{SL}(2,\mathbb{C})\) ⋮ Effective circle count for Apollonian packings and closed horospheres ⋮ The horocycle flow and the Laplacian on hyperbolic surfaces of infinite genus ⋮ Classification of joinings for Kleinian groups ⋮ Minimal sets of homogeneous flows ⋮ On the deviation of ergodic averages for horocycle flows ⋮ Horospherically invariant measures and finitely generated Kleinian groups ⋮ Anosov groups: local mixing, counting and equidistribution ⋮ Quantitative disjointness of nilflows from horospherical flows ⋮ Finitary analysis in homogeneous spaces ⋮ Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner (with an appendix by Emilio Corso) ⋮ Volume bound for the canonical lift complement of a random geodesic ⋮ Effective equidistribution of horospherical flows in infinite volume rank-one homogeneous spaces ⋮ Horospherical invariant measures and a rank dichotomy for Anosov groups ⋮ Lattice actions on the plane revisited ⋮ Polynomial effective density in quotients of \(\mathbb{H}^3\) and \(\mathbb{H}^2 \times \mathbb{H}^2\) ⋮ Working session: Thin groups and super-approximation. Abstracts from the working session held October 10--15, 2021 (hybrid meeting) ⋮ PERTURBATION OF THE SEMICLASSICAL SCHRÖDINGER EQUATION ON NEGATIVELY CURVED SURFACES ⋮ Random walks, spectral gaps, and Khintchine's theorem on fractals ⋮ Invariant distributions and time averages for horocycle flows ⋮ Horocycle Flows on Surfaces with Infinite Genus ⋮ On Omri Sarig's work on the dynamics on surfaces ⋮ An effective equidistribution result for SL(2,R)⋉(R2)⊕k and application to inhomogeneous quadratic forms ⋮ Fuchsian groups from the dynamical viewpoint ⋮ The asymptotic distribution of circles in the orbits of Kleinian groups ⋮ The horocycle flow at prime times ⋮ Deviation of ergodic averages for rational polygonal billiards ⋮ Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds ⋮ A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds ⋮ The cohomological equation and invariant distributions for horocycle maps ⋮ Totally dissipative measures for the shift and conformal \(\sigma \)-finite measures for the stable holonomies ⋮ Equidistribution and counting for orbits of geometrically finite hyperbolic groups ⋮ Apollonian circle packings: dynamics and number theory ⋮ Slow chaos in surface flows ⋮ Almost-prime times in horospherical flows on the space of lattices ⋮ On mixing and sparse ergodic theorems ⋮ Joining measures for horocycle flows on abelian covers ⋮ Mixing for smooth time-changes of general nilflows ⋮ Effective equidistribution of twisted horocycle flows and horocycle maps ⋮ Invariant measures for the horocycle flow on periodic hyperbolic surfaces ⋮ On the rate of equidistribution of expanding translates of horospheres in \(\Gamma\backslash G\) ⋮ Entropies for Negatively Curved Manifolds ⋮ Invariant measures for the horocycle flow on periodic hyperbolic surfaces ⋮ Effective Ratner theorem for SL(2,R)⋉R2 and gaps in n modulo 1 ⋮ Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces ⋮ Ergodicity of unipotent flows and Kleinian groups ⋮ The conformal measures of a normal subgroup of a cocompact Fuchsian group ⋮ Invariant Radon measures for Unipotent flows and products of Kleinian groups ⋮ Invariant measures for non-primitive tiling substitutions ⋮ Matrix coefficients, counting and primes for orbits of geometrically finite groups ⋮ An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\) ⋮ A universal divergence rate for symmetric Birkhoff Sums in infinite ergodic theory ⋮ Zero-one law for the rates of convergence in the Birkhoff ergodic theorem with continuous time

Cites Work

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• On invariant measures, minimal sets and a lemma of Margulis
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• The density at infinity of a discrete group of hyperbolic motions
• The limit set of a Fuchsian group
• Invariant measures of horospherical flows on non-compact homogeneous spaces
• Asymptotic properties of unitary representations
• Related aspects of positivity in Riemannian geometry
• The bottom of the spectrum of a Riemannian covering.
• Invariant measures for unipotent translations on homogeneous spaces.

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