Multifractal analysis of geodesic flows on surfaces without focal points

TL;DR

This paper investigates the multifractal spectra of geodesic flows on rank 1 surfaces without focal points, focusing on entropy and Hausdorff dimension estimates of Lyapunov exponent level sets.

Contribution

It generalizes existing results to compute entropy and estimate Hausdorff dimension for these flows, advancing understanding of their multifractal structure.

Findings

Computed entropy of Lyapunov level sets

Estimated Hausdorff dimension from below

Generalized results of Burns and Gelfert

Abstract

We study multifractal spectra of the geodesic flows on rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and estimate its Hausdorff dimension from below. In doing so, we employ and generalize results of Burns and Gelfert.