Equilibrium states in negative curvature
By: Frédéric Paulin, Mark Pollicott and Barbara Schapira
Contributors: Pollicott, Mark, author; Schapira, Barbara, author; Société mathématique de France
Series: Astérisque -- 373; Astérisque -- 373.
Publisher: Société mathématique de France
Published: 2015
Place of publication: Paris
Language: eng
Number of pages: 281
ISBN-13: 9782856298183
Copyright date: 2015
Subjects: Geodesic flows; Riemannian manifolds; Ergodic theory; Gibbs' equation; Curvature; Measure theory; Manifolds (Mathematics)
Description: With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. We 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.
Notes: Includes bibliographical references (unnumbered page 271-281) and index.

Summaries in English and French.