2011/04/30 by J. A. Toth, S. Zelditch
Mathematics · #math.SP
published as GAFA 23 (2013), Page 715-775 · 53 pages. Second in a series. The paper is self-contained; the methods and results are independent of the first article (arXiv:1005.1636), which dealt with Euclidean domains with ergodic billiards. Some clarifications and an appendix added extending the result to the semi-classical case
arxiv created 2012/05/01 · arxiv updated 2013/05/17
We prove that if (M, g) is a compact Riemannian manifold with ergodic geodesic flow, and if H ⊂ M is a smooth hypersurface satisfying a generic asymmetry condition with respect to the geodesic flow, then restrictions ϕj |H of an orthonormal basis \ϕj\ of Δ-eigenfunctions of (M, g) to H are quantum ergodic on H. The condition on H is satisfied by geodesic circles, closed horocycles and generic closed geodesics on a hyperbolic surface.