Polynomial decay of correlations for nonpositively curved surfaces

Trans. Amer. Math. Soc. 377 (2024) 6043-6095

Yuri Lima, Carlos Matheus and Ian Melbourne

Abstract

We prove polynomial decay of correlations for geodesic flows on a class of nonpositively curved surfaces where zero curvature only occurs along one closed geodesic. We also prove that various statistical limit laws, including the central limit theorem, are satisfied by this class of geodesic flows.