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CAMBRIDGE UNIVERSITY PRESS Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces by M. Bachir Bekka , Matthias Mayer
The study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof due to Margulis and Dani of Oppenheims conjecture. Also included here: an exposition of Ratners work on Raghunathans conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautners result on the geodesic flow of a Riemannian symmetric space; Mozes result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappiers example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.show more