首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Invariant measures for the horocycle flow on periodic hyperbolic surfaces
Authors:François Ledrappier  Omri Sarig
Institution:(1) Department of Mathematics, University of Notre-Dame, Notre-Dame, IN 46556-4618, USA;(2) Mathematics Department, Pennsylvania State University, University Park, PA 16802, USA
Abstract:We classify the ergodic invariant Radon measures for the horocycle flow on geometrically infinite regular covers of compact hyperbolic surfaces. The method is to establish a bijection between these measures and the positive minimal eigenfunctions of the Laplacian of the surface. Two consequences arise: if the group of deck transformations G is of polynomial growth, then these measures are classified by the homomorphisms from G 0 to ℝ where G 0G is a nilpotent subgroup of finite index; if the group is of exponential growth, then there may be more than one Radon measure which is invariant under the geodesic flow and the horocycle flow. We also treat regular covers of finite volume surfaces. The first author was supported by NSF grant 0500630. The second author was supported by NSF grant 0400687.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号