Journal of Modern Dynamics (JMD)

On the deviation of ergodic averages for horocycle flows

Pages: 291 - 328, Issue 2, June 2013      doi:10.3934/jmd.2013.7.291

       Abstract        References        Full Text (400.4K)       Related Articles       

Andreas Strömbergsson - Department of Mathematics, Box 480, Uppsala University, SE-75106 Uppsala, Sweden (email)

Abstract: We give effective bounds on the deviation of ergodic averages for the horocycle flow on the unit tangent bundle of a noncompact hyperbolic surface of finite area. The bounds depend on the small eigenvalues of the Laplacian and on the rate of excursion into cusps for the geodesic corresponding to the given initial point. We also prove $\Omega$-results which show that in a certain sense our bounds are essentially the best possible for any given initial point.

Keywords:  Horocycle flow, effective equidistribution, small eigenvalues.
Mathematics Subject Classification:  Primary: 37D40; Secondary: 30F35.

Received: April 2013;      Available Online: September 2013.