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Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces.
・ISBN 978-0-521-66030-3 paper GB£ 83.00
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電子版あり 大学・学術機関向け電子ブック(eBook)ISBN 978-0-511-75889-8
| 著者・編者 | Bekka, M. Bachir / Mayer, Matthias, |
|---|---|
| シリーズ | London Mathematical Society Lecture Note Series |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2000 |
| ページ数 | 212 pp. |
| 言語 | ENG |
| ニュース番号 | <M25-2034> |
解説
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.