The ergodic theory of discrete groups /:
The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been dev...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1989.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
143. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S.J. Patterson for Fuchsian groups, and later extended and refined by Sullivan. |
| Beschreibung: | 1 online resource (xi, 221 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 209-214) and index. |
| ISBN: | 9781107361577 1107361575 9780511892448 0511892446 1139884492 9781139884495 1107366488 9781107366480 1107371198 9781107371194 0511965753 9780511965753 1107364027 9781107364028 0511600674 9780511600678 |
Internformat
MARC
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| 245 | 1 | 4 | |a The ergodic theory of discrete groups / |c Peter J. Nicholls. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1989. | ||
| 300 | |a 1 online resource (xi, 221 pages) : |b illustrations | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 143 | |
| 504 | |a Includes bibliographical references (pages 209-214) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S.J. Patterson for Fuchsian groups, and later extended and refined by Sullivan. | ||
| 505 | 0 | |a Cover; Title; Copyright; Preface; Contents; CHAPTER 1; Preliminaries; 1.1 Area; 1.2 The Hyperbolic Space; 1.3 Moebius Transforms; 1.4 Discrete Groups; 1.5 The Orbital Counting Functio; 1.6 Convergence Questions; CHAPTER 2; The Limit Set; 2.1 Introduction; 2.2 The Line Transitive Set; 2.3 The Point Transitive Set; 2.4 The Conical Limit Set; 2.5 The Horospherical Limit Set; 2.6 The Dirichlet Set; 2.7 Parabolic Fixed Points; CHAPTER 3; A Measure on the Limit Set; 3.1 Construction of an Orbital Measure; 3.2 Change in Base Point; 3.3 Change of Exponent | |
| 505 | 8 | |a 3.4 Variation of Base Point and Invariance Properties3.5 The Atomic Part of the Measure; CHAPTER 4; Conformal Densitites; 4.1 Introduction; 4.2 Uniqueness; 4.3 Local Properties; 4.5 The Orbital Counting Function; 4.6 Convex Co-Compact Groups; 4.7 Summary; CHAPTER 5; Hyperbolically Harmonic Functions; 5.1 Introduction; 5.2 Harmonic Measure; 5.3 Eigenfunctions; CHAPTER 6; The Sphere at Infinity; 6.1 Introduction; 6.2 Action on S; 6.3 Action on S X S; 6.4 Action on Other Products; CHAPTER 7; Elementary Ergodic Theory; 7.1 Introduction; 7.2 The Continuous Case; 7.3 Invariant Measures; CHAPTER 8 | |
| 505 | 8 | |a The Geodesic Flow8.1 Definition; 8.2 Basic Transitivity Properties; 8.3 Ergodicity; CHAPTER 9; Geometrically Finite Groups; 9.1 Introduction; 9.2 Volume of the Line Element Space; 9.3 Hausdorff Dimension of the Limit Set; CHAPTER 10; Fuchsian Groups; 10.1 Introduction; 10.2 The Upper Half-Plane; 10.3 Geodesic and Horocyclic Flows; 10.4 The Unit Disc; 10.5 Ergodicity and Mixing; 10.6 Unique Ergodicity; 10.7 A Lattice Point Problem; REFERENCES; INDEX OF SYMBOLS; INDEX | |
| 546 | |a English. | ||
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| 650 | 6 | |a Théorie ergodique. | |
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| 776 | 0 | 8 | |i Print version: |a Nicholls, Peter J. |t Ergodic theory of discrete groups. |d Cambridge [England] ; New York : Cambridge University Press, 1989 |z 0521376742 |w (DLC) 89036118 |w (OCoLC)20012347 |
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| adam_text | |
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| author | Nicholls, Peter J. |
| author_facet | Nicholls, Peter J. |
| author_role | |
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| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| callnumber-raw | QA313 .N53 1989eb |
| callnumber-search | QA313 .N53 1989eb |
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| contents | Cover; Title; Copyright; Preface; Contents; CHAPTER 1; Preliminaries; 1.1 Area; 1.2 The Hyperbolic Space; 1.3 Moebius Transforms; 1.4 Discrete Groups; 1.5 The Orbital Counting Functio; 1.6 Convergence Questions; CHAPTER 2; The Limit Set; 2.1 Introduction; 2.2 The Line Transitive Set; 2.3 The Point Transitive Set; 2.4 The Conical Limit Set; 2.5 The Horospherical Limit Set; 2.6 The Dirichlet Set; 2.7 Parabolic Fixed Points; CHAPTER 3; A Measure on the Limit Set; 3.1 Construction of an Orbital Measure; 3.2 Change in Base Point; 3.3 Change of Exponent 3.4 Variation of Base Point and Invariance Properties3.5 The Atomic Part of the Measure; CHAPTER 4; Conformal Densitites; 4.1 Introduction; 4.2 Uniqueness; 4.3 Local Properties; 4.5 The Orbital Counting Function; 4.6 Convex Co-Compact Groups; 4.7 Summary; CHAPTER 5; Hyperbolically Harmonic Functions; 5.1 Introduction; 5.2 Harmonic Measure; 5.3 Eigenfunctions; CHAPTER 6; The Sphere at Infinity; 6.1 Introduction; 6.2 Action on S; 6.3 Action on S X S; 6.4 Action on Other Products; CHAPTER 7; Elementary Ergodic Theory; 7.1 Introduction; 7.2 The Continuous Case; 7.3 Invariant Measures; CHAPTER 8 The Geodesic Flow8.1 Definition; 8.2 Basic Transitivity Properties; 8.3 Ergodicity; CHAPTER 9; Geometrically Finite Groups; 9.1 Introduction; 9.2 Volume of the Line Element Space; 9.3 Hausdorff Dimension of the Limit Set; CHAPTER 10; Fuchsian Groups; 10.1 Introduction; 10.2 The Upper Half-Plane; 10.3 Geodesic and Horocyclic Flows; 10.4 The Unit Disc; 10.5 Ergodicity and Mixing; 10.6 Unique Ergodicity; 10.7 A Lattice Point Problem; REFERENCES; INDEX OF SYMBOLS; INDEX |
| ctrlnum | (OCoLC)839304809 |
| 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 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839304809 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:22Z |
| institution | BVB |
| isbn | 9781107361577 1107361575 9780511892448 0511892446 1139884492 9781139884495 1107366488 9781107366480 1107371198 9781107371194 0511965753 9780511965753 1107364027 9781107364028 0511600674 9780511600678 |
| language | English |
| oclc_num | 839304809 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xi, 221 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Nicholls, Peter J. The ergodic theory of discrete groups / Peter J. Nicholls. Cambridge [England] ; New York : Cambridge University Press, 1989. 1 online resource (xi, 221 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 143 Includes bibliographical references (pages 209-214) and index. Print version record. The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S.J. Patterson for Fuchsian groups, and later extended and refined by Sullivan. Cover; Title; Copyright; Preface; Contents; CHAPTER 1; Preliminaries; 1.1 Area; 1.2 The Hyperbolic Space; 1.3 Moebius Transforms; 1.4 Discrete Groups; 1.5 The Orbital Counting Functio; 1.6 Convergence Questions; CHAPTER 2; The Limit Set; 2.1 Introduction; 2.2 The Line Transitive Set; 2.3 The Point Transitive Set; 2.4 The Conical Limit Set; 2.5 The Horospherical Limit Set; 2.6 The Dirichlet Set; 2.7 Parabolic Fixed Points; CHAPTER 3; A Measure on the Limit Set; 3.1 Construction of an Orbital Measure; 3.2 Change in Base Point; 3.3 Change of Exponent 3.4 Variation of Base Point and Invariance Properties3.5 The Atomic Part of the Measure; CHAPTER 4; Conformal Densitites; 4.1 Introduction; 4.2 Uniqueness; 4.3 Local Properties; 4.5 The Orbital Counting Function; 4.6 Convex Co-Compact Groups; 4.7 Summary; CHAPTER 5; Hyperbolically Harmonic Functions; 5.1 Introduction; 5.2 Harmonic Measure; 5.3 Eigenfunctions; CHAPTER 6; The Sphere at Infinity; 6.1 Introduction; 6.2 Action on S; 6.3 Action on S X S; 6.4 Action on Other Products; CHAPTER 7; Elementary Ergodic Theory; 7.1 Introduction; 7.2 The Continuous Case; 7.3 Invariant Measures; CHAPTER 8 The Geodesic Flow8.1 Definition; 8.2 Basic Transitivity Properties; 8.3 Ergodicity; CHAPTER 9; Geometrically Finite Groups; 9.1 Introduction; 9.2 Volume of the Line Element Space; 9.3 Hausdorff Dimension of the Limit Set; CHAPTER 10; Fuchsian Groups; 10.1 Introduction; 10.2 The Upper Half-Plane; 10.3 Geodesic and Horocyclic Flows; 10.4 The Unit Disc; 10.5 Ergodicity and Mixing; 10.6 Unique Ergodicity; 10.7 A Lattice Point Problem; REFERENCES; INDEX OF SYMBOLS; INDEX English. Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Théorie ergodique. Groupes discrets. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Discrete groups fast Ergodic theory fast Diskrete Gruppe gnd http://d-nb.info/gnd/4135541-6 Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram Print version: Nicholls, Peter J. Ergodic theory of discrete groups. Cambridge [England] ; New York : Cambridge University Press, 1989 0521376742 (DLC) 89036118 (OCoLC)20012347 London Mathematical Society lecture note series ; 143. 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=552398 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552398 Volltext |
| spellingShingle | Nicholls, Peter J. The ergodic theory of discrete groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Preface; Contents; CHAPTER 1; Preliminaries; 1.1 Area; 1.2 The Hyperbolic Space; 1.3 Moebius Transforms; 1.4 Discrete Groups; 1.5 The Orbital Counting Functio; 1.6 Convergence Questions; CHAPTER 2; The Limit Set; 2.1 Introduction; 2.2 The Line Transitive Set; 2.3 The Point Transitive Set; 2.4 The Conical Limit Set; 2.5 The Horospherical Limit Set; 2.6 The Dirichlet Set; 2.7 Parabolic Fixed Points; CHAPTER 3; A Measure on the Limit Set; 3.1 Construction of an Orbital Measure; 3.2 Change in Base Point; 3.3 Change of Exponent 3.4 Variation of Base Point and Invariance Properties3.5 The Atomic Part of the Measure; CHAPTER 4; Conformal Densitites; 4.1 Introduction; 4.2 Uniqueness; 4.3 Local Properties; 4.5 The Orbital Counting Function; 4.6 Convex Co-Compact Groups; 4.7 Summary; CHAPTER 5; Hyperbolically Harmonic Functions; 5.1 Introduction; 5.2 Harmonic Measure; 5.3 Eigenfunctions; CHAPTER 6; The Sphere at Infinity; 6.1 Introduction; 6.2 Action on S; 6.3 Action on S X S; 6.4 Action on Other Products; CHAPTER 7; Elementary Ergodic Theory; 7.1 Introduction; 7.2 The Continuous Case; 7.3 Invariant Measures; CHAPTER 8 The Geodesic Flow8.1 Definition; 8.2 Basic Transitivity Properties; 8.3 Ergodicity; CHAPTER 9; Geometrically Finite Groups; 9.1 Introduction; 9.2 Volume of the Line Element Space; 9.3 Hausdorff Dimension of the Limit Set; CHAPTER 10; Fuchsian Groups; 10.1 Introduction; 10.2 The Upper Half-Plane; 10.3 Geodesic and Horocyclic Flows; 10.4 The Unit Disc; 10.5 Ergodicity and Mixing; 10.6 Unique Ergodicity; 10.7 A Lattice Point Problem; REFERENCES; INDEX OF SYMBOLS; INDEX Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Théorie ergodique. Groupes discrets. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Discrete groups fast Ergodic theory fast Diskrete Gruppe gnd http://d-nb.info/gnd/4135541-6 Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044600 http://id.loc.gov/authorities/subjects/sh85038369 http://d-nb.info/gnd/4135541-6 http://d-nb.info/gnd/4015246-7 |
| title | The ergodic theory of discrete groups / |
| title_auth | The ergodic theory of discrete groups / |
| title_exact_search | The ergodic theory of discrete groups / |
| title_full | The ergodic theory of discrete groups / Peter J. Nicholls. |
| title_fullStr | The ergodic theory of discrete groups / Peter J. Nicholls. |
| title_full_unstemmed | The ergodic theory of discrete groups / Peter J. Nicholls. |
| title_short | The ergodic theory of discrete groups / |
| title_sort | ergodic theory of discrete groups |
| topic | Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Théorie ergodique. Groupes discrets. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Discrete groups fast Ergodic theory fast Diskrete Gruppe gnd http://d-nb.info/gnd/4135541-6 Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram |
| topic_facet | Ergodic theory. Discrete groups. Théorie ergodique. Groupes discrets. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Discrete groups Ergodic theory Diskrete Gruppe Ergodentheorie |
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| work_keys_str_mv | AT nichollspeterj theergodictheoryofdiscretegroups AT nichollspeterj ergodictheoryofdiscretegroups |