Topic
Horocycle
About: Horocycle is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4463 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1991
TL;DR: In this paper, Beardon et al. introduce hyperbolic geometry, including geodesic flows, interval maps, and symbolic dynamics, and present a measure on the limit set of a discrete group.
Abstract: Alan F. Beardon: An introduction to hyperbolic geometry Michael Keane: Ergodic theory and subshifts of finite type Anthony Manning: Dynamics of geodesic and horocycle flows on surfaces of constant negative curvature Roy L. Adler: Geodesic flows, interval maps, and symbolic dynamics Caroline Series: Geometrical methods of symbolic coding Mark Pollicott: Closed geodesics and zeta functions Dieter H. Mayer: Continued fractions and related transformations Steven P. Lalley: Probabilistic methods in certain counting problems of ergodic theory Peter J. Nicholls: A measure on the limit set of a discrete group Etienne Ghys & Pierre de la Harpe: Infinite groups as geometric objects (after Gromov) James W. Cannon: The theory of negatively curved spaces and groups
368 citations
TL;DR: In this article, the authors study the Sobolev regularity of these obstructions, construct smooth solutions of the cohomological equation, and derive asymptotics for the ergodic averages of horocycle flows.
Abstract: There are infinitely many obstructions to the existence of smooth solutions of the cohomological equation Uu=f, where U is the vector field generating the horocycle flow on the unit tangent bundle SM of a Riemann surface M of finite area and f is a given function on SM. We study the Sobolev regularity of these obstructions, construct smooth solutions of the cohomological equation, and derive asymptotics for the ergodic averages of horocycle flows.
205 citations
181 citations
TL;DR: In this article, it is shown that if C is the cone of positive N-invariant Radon measures in the space of all radon measures with the vague topology, then C is a closed convex hull of the union of its extremal generators.
Abstract: acts on T S. It is our main goal to determine all N-invariant Radon measures on T1S. Our first remark is that if C is the cone of positive N-invariant Radon measures in the space ’(Tx S) of all Radon measures with the vague topology, then C is the closed convex hull of the union of its extremal generators [B, II No. 2]; moreover it is easily seen that a measure is on an extremal generator of C if and only if it is ergodic. This reduces the problem to the classification of all ergodic measures. To proceed further we consider the following decomposition of T S: Let S be the ideal boundary of D and A c S be the limit set of F. Using the visual map:
147 citations
TL;DR: In this article, the notion of unique ergodicity is extended to multidimensional foliations, and it is shown that ifg is the strong stable or strong unstable foliation of a topologically mixing basic set Ωκ for an Axiom A diffeomorphism or flow theng is uniquely ergodic.
Abstract: The notion of unique ergodicity is extended to multidimensional foliations, and it is shown that ifg is the strong stable or strong unstable foliation of a topologically mixing basic set Ωκ for an Axiom A diffeomorphism or flow theng is uniquely ergodic
141 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 13 |
| 2020 | 13 |
| 2019 | 17 |
| 2018 | 14 |
| 2017 | 8 |
| 2016 | 20 |