Ruelle resonances: Geodesic Flow on Noncompact Manifolds

This lecture by Sébastien Gouézel focuses on the analog of machinery developed for geodesic flows on noncompact manifolds with negative curvature. The instructor presents a theorem in the context of geodesic flows, emphasizing the importance of curvature and the assumption of non-elementary manifolds. The discussion delves into the dynamics of geodesic flows, Gibbs measures, pressures, and real resonances, highlighting the differences from the toy model. The lecture explores the concept of pressure at infinity, Gibbs measures, and the construction of measures on stable and unstable manifolds. The instructor also touches upon the notion of Margulis function and the expectation of sharp bounds for resonances, drawing parallels with Laplacian spectra.