Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

ISBN-13: 9780521660303 / Angielski / Miękka / 2000 / 212 str.

B. Bekka; M. Bachir Bekka; M. Mayer

Opis

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.

Recenzje

'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

Spis treści

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.