| Description |
1 online resource (x, 200 pages) : illustrations |
| Series |
London Mathematical Society lecture note series ; 269 |
|
London Mathematical Society lecture note series ; 269.
|
| Contents |
Ergodic Systems -- Examples and Basic Results -- Ergodic Theory and Unitary Representations -- Invariant Measures and Unique Ergodicity -- The Geodesic Flow of Riemannian Locally Symmetric Spaces -- Some Hyperbolic Geometry -- Lattices and Fundamental Domains -- The Geodesic Flow of Compact Riemann Surfaces -- The Geodesic Flow on Riemannian Locally Symmetric Spaces -- The Vanishing Theorem of Howe and Moore -- Howe--Moore's Theorem -- Moore's Ergodicity Theorems -- Counting Lattice Points in the Hyperbolic Plane -- Mixing of All Orders -- The Horocycle Flow -- The Horocycle Flow of a Riemann Surface -- Proof of Hedlund's Theorem--Cocompact Case -- Classification of Invariant Measures -- Equidistribution of Horocycle Orbits -- Siegel Sets, Mahler's Criterion and Margulis' Lemma -- Siegel Sets in SL(n, R) -- SL(n, Z) is a lattice in SL(n, R) -- Mahler's Criterion -- Reduction of Positive Definite Quadratic Forms -- Margulis' Lemma -- An Application to Number Theory: Oppenheim's Conjecture -- Oppenheim's Conjecture -- Proof of the Theorem--Preliminaries -- Existence of Minimal Closed Subsets -- Orbits of One-Parameter Groups of Unipotent Linear Transformations -- Proof of the Theorem--Conclusion -- Ratner's Results on the Conjectures of Raghunathan, Dani and Margulis |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 189-197) and index |
| Notes |
English |
|
Print version record |
| Subject |
Ergodic theory.
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Topological dynamics.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Ergodic theory
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Topological dynamics
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Ergodiciteit.
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Topologische groepen.
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Dynamische systemen.
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Théorie ergodique.
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Dynamique topologique.
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| Form |
Electronic book
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| Author |
Mayer, Matthias (Mathematician)
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| ISBN |
9781107089273 |
|
1107089271 |
|
9780511758898 |
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0511758898 |
|
9781107101104 |
|
1107101107 |
|
9781107095502 |
|
1107095506 |
|
1299748945 |
|
9781299748941 |
|
1139885561 |
|
9781139885560 |
|
1107092256 |
|
9781107092259 |
|
1107103592 |
|
9781107103597 |
|
