UID:
almafu_9959234618302883
Format:
1 online resource (xi, 221 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88449-2
,
1-107-36648-8
,
1-107-37119-8
,
1-107-36157-5
,
0-511-96575-3
,
1-299-40426-X
,
1-107-36402-7
,
0-511-89244-6
,
0-511-60067-4
Series Statement:
London Mathematical Society lecture note series ; 143
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
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
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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
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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
Additional Edition:
ISBN 0-521-37674-2
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511600678
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