Preprint, December 2025
Yuri Lima, Carlos Matheus and Ian Melbourne
Abstract
We prove a nonstandard central limit theorem and weak invariance principle,
with superdiffusive normalisation (t log t)1/2, for geodesic flows on a class of nonpositively curved
surfaces with flat cylinder. We also prove that correlations decay at rate t-1.
An important ingredient of the proof, which is of independent interest, is an improved
results on the regularity of the stable/unstable foliations induced by the Green bundles.