Symbolic dynamics for the geodesic flow on locally symmetric good orbifolds of rank one / Anke D. Pohl. 2009
Content
- 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 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
- 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
- The base manifold of the cross sections
- Precells and cells in SH
- Geometric symbolic dynamics
- Reduction and arithmetic symbolic dynamics
- Transfer operators
- The modular surface
- Bibliography
- Index of Notations
- Index of Definitions and Terminology