VARIATIONS ON A THEOREM OF BIRMAN AND SERIES

Suppose that Sigma is a hyperbolic surface and f : R+ -> R+ a monotonic function. We study the closure in the projective tangent bundle PT Sigma of the set of all geodesics gamma satisfying i(gamma, gamma) <= f (l(Sigma)(gamma)). For instance we prove that if f is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3.