Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

M. Bachir Bekka (Author), Matthias Mayer (Author)

9780521660303, Cambridge University Press

Paperback, published 11 May 2000

212 pages, 11 b/w illus. 16 exercises
22.9 x 15.2 x 1.2 cm, 0.305 kg

'This book can be used as a guide to modern ergodic theory and dynamics. It can be used by graduate students and by researchers in different areas, since the contents of the book range from elementary results to modern theories.' EMS

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 Oppenheim's conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's 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; Ledrappier's 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.

1. Ergodic systems
2. The geodesic flow of Riemannian locally symmetric spaces
3. The vanishing theorem of Howe and Moore
4. The horocycle flow
5. Siegel sets, Mahler's criterion and Margulis' lemma
6. An application to number theory: Oppenheim's conjecture.

Subject Areas: Probability & statistics [PBT], Topology [PBP], Geometry [PBM]