Abstract

In this article, we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow for any complete, pinched negatively curved Riemannian manifold. Furthermore, we prove that the entropy of a (Formula presented.) -finite, infinite, ergodic and conservative invariant measure is bounded from above by the entropy at infinity of the geodesic flow. © 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.