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Symbolic dynamics for the geodesic flow on locally symmetric good orbifolds of rank one / Anke D. Pohl. 2009
Inhalt
Abstract
Zusammenfassung
Acknowledgements
Introduction
Isometric fundamental regions
Classification-free constructions
H-type algebras and the J2-condition
C-module structures and the J2-condition
Bijection between H-type algebras and C-module structures
Construction of symmetric spaces
The model D
The ball model B
The Cayley transform
The map 2
The isometry group
Isometric fundamental regions
The Cauchy-Schwarz Theorem for 2
H-coordinates, Cygan metric, and isometric spheres
Fundamental region
Projective models
Division algebras induced by J2C-module structures
Projective construction in the associative cases
C-sesquilinear hermitian forms
The C-projective space PC(E)
The C-hyperbolic spaces PC(E-(1)) and PC(E-(2))
Isometric spheres via cocycles
A special instance of Theorem 2.3.4
Isometric spheres and isometric fundamental regions in the literature
Real hyperbolic spaces
Complex hyperbolic spaces
Quaternionic hyperbolic spaces
Cusp expansion
Preliminaries
Symbolic dynamics
Cusp expansion
Isometric fundamental domains
Isometric spheres
Type (O)
Type (F)
The set K and isometric fundamental domains
Relevant sets and the boundary structure of K
The structure of the isometric fundamental domains
A characterization of the group
Precells in H
Boundary intervals
Precells in H and basal families
The tesselation of H by basal families of precells
A group that does not satisfy (A2)
Cells in H
Cycles in A
Cells in H and their properties
The base manifold of the cross sections
Precells and cells in SH
Geometric symbolic dynamics
Geometric cross section
Geometric coding sequences and geometric symbolic dynamics
Reduction and arithmetic symbolic dynamics
Reduced cross section
Reduced coding sequences and arithmetic symbolic dynamics
Generating function for the future part
Transfer operators
The modular surface
The normalized symbolic dynamics
The work of Series
Bibliography
Index of Notations
Index of Definitions and Terminology
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