Title: A Birman-Series result for infinitely self-intersecting geodesics on surfaces

Abstract: Let S be a hyperbolic surface. Birman and Series showed that there is a single nowhere dense, Hausdorff dimension 1 subset of S that contains the images of all complete (bi-infinite) simple geodesics. We examine sets of geodesics with different possible self-intersection rates and show that the Birman-Series type result holds for all of the sets where the rate is o(l^2) intersections per length l subarc. In contrast, the set of geodesics with the maximal possible self-intersection rate, which is k l^2, is dense and has full Hausdorff dimension in S.