Geodesic flows in manifolds of nonpositive curvature (Q2778787)

This is an excellent survey of geodesic flows on spaces of non-positive sectional curvature, including symmetric and locally symmetric spaces. It starts with a historical survey and then gives some preliminaries on Riemannian manifolds, manifolds of non-positive curvature (including Cartan-Hadamard and Cartan fixed point theorems), the sphere at infinity of such simply connected manifolds, and measures on such spheres at infinity (including harmonic and Patterson-Sullivan measures). The main focus of the paper is on some outstanding problems in geometry and dynamics of manifolds of non-positive curvature related to Anosov foliations, Katok entropy conjecture, geodesic conjugacy problem, harmonic and asymptotically harmonic spaces and rigidity. The last part of the paper discusses the work of \textit{G. Besson, G. Courtois} and \textit{S. Gallot} [Geom. Funct. Anal. 5, 731-799 (1995; Zbl 0851.53032) and Ergodic Theory Dyn. Syst. 16, 623-649 (1996; Zbl 0887.58030)] and its corollaries that unified the earlier results and settled a number of remaining open problems.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00044].