Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces
Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces
CAD$98.95
The study of geodesic flows on homogeneous spaces is an area of research that has recently yielded some fascinating developments. This book focuses on many of these, with one of its highlights an elementary and complete proof by Margulis and Dani of Oppenheim's conjecture. Other features are self-contained treatments of 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; and Ledrappier's example of a mixing action which is not a mixing of all orders.
- No other books cover this material
- Area is of much interest to researchers
- Complete introduction is given for the more advanced topics needed for understanding new developments in this field
Reviews & endorsements
'… a most welcome introduction to the study of group actions on homogenous spaces … I highly recommend the book.' Sanju Velani, Bulletin of the London Mathematical Society
'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
Product details
August 2000Paperback
9780521660303
212 pages
229 × 152 × 12 mm
0.305kg
11 b/w illus. 16 exercises
Available
Table of Contents
- 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.
