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排序方式: 共有59条查询结果,搜索用时 15 毫秒
1.
In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon's definition of intersection forms for surfaces.
2.
In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher. 相似文献
3.
François Ledrappier Mark Pollicott 《Bulletin of the Brazilian Mathematical Society》2005,36(2):143-176
In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚp) on ℚp × ℚp and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually
associated to GL(2,ℚp)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension
of the geodesic flow. 相似文献
4.
In this article we extend well-known results of Livsic on theregularity of measurable solutions to the cocycle equation.Livsic proved a regularity result for real valued cocycles,but for compact Lie group valued cocycles his result was restrictedto coboundaries (that is, trivial or constant cocycles). Inthis article we prove the complete result. We present several useful applications of these results. 相似文献
5.
Mark Pollicott 《Topology and its Applications》2007,154(12):2365-2375
We study lifts of the stable foliation of a pseudo-Anosov diffeomorphism to abelian covers. Under certain conditions, we show that it is ergodic but not uniquely ergodic and describe the ergodic measures. 相似文献
6.
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8.
Mark Pollicott 《Communications in Mathematical Physics》1987,113(1):137-154
For the strong unstable foliation (or horocycle foliation) of an Anosov flow there exists a unique transverse measure called the Margulis measure. In this paper we extend Margulis' results to more general transverse distributions for the foliation. As an application we derive our main result: The non-zero analytic extension to a strip of the Selberg zeta function for compact surfaces of constant negative curvature persists under small perturbations in the metric. There is an equivalent formulation in terms of the Fourier transform of the correlation function. 相似文献
9.
Mark Pollicott 《Transactions of the American Mathematical Society》2003,355(8):3241-3252
We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus . This describes the set of unit tangent vectors for which the associated orbit has a given asymptotic cycle in homology.
10.
In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic
estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals.
Related pair correlation problems have been studied in both Quantum Chaos and number theory. 相似文献