For directions to UK, please see the Campus Guide . On the other hand if the classical motion is chaotic, much less is known. In this talk, I will describe the role it played in some PDE problems in higher-dimensional manifolds. In particular, I will consider analytic plane domains and surfaces of revolution, where the unknown is a real analytic function of one variable. L oo -norms bounded independently of the eigenvalue.
Similar bases exist on other flat manifolds.
The known connections between eigenfunctions of the Laplacian and the dynamics of the geodesic flow are not strong enough at present to answer these questions in the general setting of compact Riemannian manifolds. Let G be a discrete convex cocompact subgroup of the group G of its orientation preserving isometries. We consider the limit set L of G , a subset of the boundary of B . Possible generalizations of the results to arbitrary geometrically finite groups are discussed. Most of the material presented in the talk is based on joint work with Ulrich Bunke.