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ISSN 1079-6762

 

Invariant measures for the horocycle flow on periodic hyperbolic surfaces


Authors: François Ledrappier and Omri Sarig
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 89-94
MSC (2000): Primary 37D40, 37A40; Secondary 31C12
Published electronically: November 15, 2005
MathSciNet review: 2183007
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Abstract: We describe the ergodic invariant Radon measures for the horocycle flow on general (infinite) regular covers of finite volume hyperbolic surfaces. The method is to establish a bijection between these measures and the positive minimal eigenfunctions of the Laplacian of the covering surface.


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Additional Information

François Ledrappier
Affiliation: Department of Mathematics, University of Notre-Dame, Notre-Dame, IN 46556-4618
Email: ledrappier.1@nd.edu

Omri Sarig
Affiliation: Mathematics Department, Pennsylvania State University, University Park, PA 16802
Email: sarig@math.psu.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-05-00151-4
PII: S 1079-6762(05)00151-4
Received by editor(s): July 27, 2005
Published electronically: November 15, 2005
Additional Notes: F.L. is supported by NSF grant DMS-0400687
O.S. is supported by NSF grant DMS-0500630
Dedicated: Pour Martine
Communicated by: Boris Hasselblatt
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.