Description
Book SynopsisA monograph devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration.
Table of Contents
- Introduction
- Thurston maps
- Lattes maps
- Quasiconformal and rough geometry
- Cell decompositions
- Expansion
- Thurston maps with two or three postcritical points
- Visual metrics
- Symbolic dynamics
- Tile graphs
- Isotopies
- Subdivisions
- Quotients of Thurston maps
- Combinatorially expanding Thurston maps
- Invariant curves
- The combinatorial expansion factor
- The measure of maximal entropy
- The geometry of the visual sphere
- Rational Thurston maps and Lebesgue measure
- A combinatorial characterization of Lattes maps
- Outlook and open problems
- Appendix A
- Bibliography
- Index.
