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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1989.
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| Colección: | London Mathematical Society lecture note series ;
143. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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