Equilibrium States in Negative Curvature

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools for studying the ergodic theory of the geodesic flow on negatively curved manifolds. The authors develop a framework (through Patterson-Sullivan densities) that allows them to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. They give many applications, to the variational principle, the counting and equidistribution of orbit points and periods, the unique ergodicity of the strong unstable foliation and the classification of Gibbs densities on some Riemannian covers.