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arXiv · 2512.11051

Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces

Yuri Lima·Carlos Matheus·Ian Melbourne
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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.

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Yuri Lima, Carlos Matheus, Ian Melbourne. 2025-12-11. Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces. https://arxiv.org/abs/2512.11051

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