On statistical properties of geodesic flows on negatively curved surfaces

We use thermodynamic formalism to prove exponential decay of correlations for Feynman-Kac semigroups over geodesic flows on negatively curved surfaces. This result implies sharp bounds on error term in several limit theorems including mixing of horocycle flow, equidistribution of large circle, hyperbolic lattice problem and prime orbit theorem. The second part of the work is devoted to the application of thermodynamic formalism to the study of geodesic excursions.