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Paper

Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces

Abstract

We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation , for geodesic flows on a class of nonpositively curved surfaces with flat cylinder. We also prove that correlations decay at rate . 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.