Variations on a Theorem of Birman and Series

Suppose that $Σ$ is a hyperbolic surface and $f:\mathbb R_+\to\mathbb R_+$ a monotonic function. We study the closure in the projective tangent bundle $PTΣ$ of the set of all geodesics $γ$ satisfying $I(γ,γ)\leq f(\ell_Σ(γ))$. For instance we prove that if $f$ is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3.

No reviews yet.

No comments yet.