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: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York :
Cambridge University Press,
2000.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
269. |
| Schlagworte: | |
| Online-Zugang: | 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: | 1 online resource (x, 200 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 189-197) and index. |
| ISBN: | 9781107089273 1107089271 9780511758898 0511758898 9781107101104 1107101107 9781107095502 1107095506 1299748945 9781299748941 1139885561 9781139885560 1107092256 9781107092259 1107103592 9781107103597 |
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| 505 | 0 | 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. |
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 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. | ||
| 650 | 0 | |a Ergodic theory. |0 http://id.loc.gov/authorities/subjects/sh85044600 | |
| 650 | 0 | |a Topological dynamics. |0 http://id.loc.gov/authorities/subjects/sh85136080 | |
| 650 | 6 | |a Théorie ergodique. | |
| 650 | 6 | |a Dynamique topologique. | |
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| 700 | 1 | |a Mayer, Matthias |c (Mathematician) |1 https://id.oclc.org/worldcat/entity/E39PCjvFxh3c3R9Vdw8TpFV4pX |0 http://id.loc.gov/authorities/names/nb2015003417 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn852898462 |
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| _version_ | 1816882238467342336 |
| adam_text | |
| any_adam_object | |
| author | Bekka, M. Bachir |
| author2 | Mayer, Matthias (Mathematician) |
| author2_role | |
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| author_GND | http://id.loc.gov/authorities/names/nb2015003417 |
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| callnumber-search | QA611.5 .B42 2000eb |
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| collection | ZDB-4-EBA |
| 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 | (OCoLC)852898462 |
| 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 |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn852898462 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:26Z |
| institution | BVB |
| isbn | 9781107089273 1107089271 9780511758898 0511758898 9781107101104 1107101107 9781107095502 1107095506 1299748945 9781299748941 1139885561 9781139885560 1107092256 9781107092259 1107103592 9781107103597 |
| language | English |
| oclc_num | 852898462 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 200 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Bekka, M. Bachir. Ergodic theory and topological dynamics of group actions on homogeneous spaces / M. Bachir Bekka, Matthias Mayer. Cambridge, U.K. ; New York : Cambridge University Press, 2000. 1 online resource (x, 200 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 269 Includes bibliographical references (pages 189-197) and index. 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. Print version record. English. 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. http://id.loc.gov/authorities/subjects/sh85044600 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Théorie ergodique. Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Ergodiciteit. gtt Topologische groepen. gtt Dynamische systemen. gtt Théorie ergodique. ram Dynamique topologique. ram Mayer, Matthias (Mathematician) https://id.oclc.org/worldcat/entity/E39PCjvFxh3c3R9Vdw8TpFV4pX http://id.loc.gov/authorities/names/nb2015003417 Print version: Bekka, M. Bachir. Ergodic theory and topological dynamics of group actions on homogeneous spaces. Cambridge, U.K. ; New York : Cambridge University Press, 2000 0521660300 (DLC) 00708882 (OCoLC)42790871 London Mathematical Society lecture note series ; 269. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569302 Volltext |
| spellingShingle | Bekka, M. Bachir Ergodic theory and topological dynamics of group actions on homogeneous spaces / London Mathematical Society lecture note series ; 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. http://id.loc.gov/authorities/subjects/sh85044600 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Théorie ergodique. Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Ergodiciteit. gtt Topologische groepen. gtt Dynamische systemen. gtt Théorie ergodique. ram Dynamique topologique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044600 http://id.loc.gov/authorities/subjects/sh85136080 |
| title | Ergodic theory and topological dynamics of group actions on homogeneous spaces / |
| title_alt | 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. http://id.loc.gov/authorities/subjects/sh85044600 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Théorie ergodique. Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Ergodiciteit. gtt Topologische groepen. gtt Dynamische systemen. gtt Théorie ergodique. ram Dynamique topologique. ram |
| topic_facet | Ergodic theory. Topological dynamics. Théorie ergodique. Dynamique topologique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Ergodic theory Topological dynamics Ergodiciteit. Topologische groepen. Dynamische systemen. |
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| work_keys_str_mv | AT bekkambachir ergodictheoryandtopologicaldynamicsofgroupactionsonhomogeneousspaces AT mayermatthias ergodictheoryandtopologicaldynamicsofgroupactionsonhomogeneousspaces |