Ergodic theory and topological dynamics of group actions on homogeneous spaces:
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 conjectur...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2000
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| Schriftenreihe: | London Mathematical Society lecture note series
269 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 200 pages) |
| ISBN: | 9780511758898 |
| DOI: | 10.1017/CBO9780511758898 |
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| 245 | 1 | 0 | |a Ergodic theory and topological dynamics of group actions on homogeneous spaces |c M. Bachir Bekka, Matthias Mayer |
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| 505 | 8 | 0 | |t Ergodic Systems |t Examples and Basic Results |t Ergodic Theory and Unitary Representations |t Invariant Measures and Unique Ergodicity |t The Geodesic Flow of Riemannian Locally Symmetric Spaces |t Some Hyperbolic Geometry |t Lattices and Fundamental Domains |t The Geodesic Flow of Compact Riemann Surfaces |t The Geodesic Flow on Riemannian Locally Symmetric Spaces |t The Vanishing Theorem of Howe and Moore |t Howe--Moore's Theorem |t Moore's Ergodicity Theorems |t Counting Lattice Points in the Hyperbolic Plane |t Mixing of All Orders |t The Horocycle Flow |t The Horocycle Flow of a Riemann Surface |t Proof of Hedlund's Theorem--Cocompact Case |t Classification of Invariant Measures |t Equidistribution of Horocycle Orbits |t Siegel Sets, Mahler's Criterion and Margulis' Lemma |t Siegel Sets in SL(n, R) |t SL(n, Z) is a lattice in SL(n, R) |t Mahler's Criterion |t Reduction of Positive Definite Quadratic Forms |t Margulis' Lemma |t An Application to Number Theory: Oppenheim's Conjecture |t Oppenheim's Conjecture |t Proof of the Theorem--Preliminaries |t Existence of Minimal Closed Subsets |t Orbits of One-Parameter Groups of Unipotent Linear Transformations |t Proof of the Theorem--Conclusion |t Ratner's Results on the Conjectures of Raghunathan, Dani and Margulis |
| 520 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804176884236288000 |
|---|---|
| any_adam_object | |
| author | Bekka, M. Bachir |
| author_facet | Bekka, M. Bachir |
| author_role | aut |
| author_sort | Bekka, M. Bachir |
| author_variant | m b b mb mbb |
| building | Verbundindex |
| bvnumber | BV043941926 |
| classification_rvk | SK 350 SK 810 SK 820 |
| collection | ZDB-20-CBO |
| 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511758898 (OCoLC)855562740 (DE-599)BVBBV043941926 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511758898 |
| format | Electronic eBook |
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| id | DE-604.BV043941926 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511758898 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350896 |
| oclc_num | 855562740 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 200 pages) |
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| publishDate | 2000 |
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| publisher | Cambridge University Press |
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| spelling | Bekka, M. Bachir Verfasser aut Ergodic theory and topological dynamics of group actions on homogeneous spaces M. Bachir Bekka, Matthias Mayer Ergodic Theory & Topological Dynamics of Group Actions on Homogeneous Spaces Cambridge Cambridge University Press 2000 1 online resource (x, 200 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 269 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Ergodic theory Topological dynamics Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Topologische Dynamik (DE-588)4253345-4 s 1\p DE-604 Mayer, Matthias Sonstige oth Erscheint auch als Druckausgabe 978-0-521-66030-3 https://doi.org/10.1017/CBO9780511758898 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bekka, M. Bachir Ergodic theory and topological dynamics of group actions on homogeneous spaces 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 Ergodic theory Topological dynamics Ergodentheorie (DE-588)4015246-7 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4253345-4 |
| title | Ergodic theory and topological dynamics of group actions on homogeneous spaces |
| title_alt | Ergodic Theory & Topological Dynamics of Group Actions on Homogeneous Spaces 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 |
| title_auth | Ergodic theory and topological dynamics of group actions on homogeneous spaces |
| title_exact_search | Ergodic theory and topological dynamics of group actions on homogeneous spaces |
| title_full | Ergodic theory and topological dynamics of group actions on homogeneous spaces M. Bachir Bekka, Matthias Mayer |
| title_fullStr | Ergodic theory and topological dynamics of group actions on homogeneous spaces M. Bachir Bekka, Matthias Mayer |
| title_full_unstemmed | Ergodic theory and topological dynamics of group actions on homogeneous spaces M. Bachir Bekka, Matthias Mayer |
| title_short | Ergodic theory and topological dynamics of group actions on homogeneous spaces |
| title_sort | ergodic theory and topological dynamics of group actions on homogeneous spaces |
| topic | Ergodic theory Topological dynamics Ergodentheorie (DE-588)4015246-7 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| topic_facet | Ergodic theory Topological dynamics Ergodentheorie Topologische Dynamik |
| url | https://doi.org/10.1017/CBO9780511758898 |
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