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OverviewThe 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. Full Product DetailsAuthor: M. Bachir Bekka (Université de Metz, France) , Matthias Mayer (KPMG, Münich)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) ISBN: 9780511758898ISBN 10: 0511758898 Publication Date: 05 August 2013 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of Contents1. 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.Reviews'… 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 '... 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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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