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Expanding Thurston Maps
About this Title
Mario Bonk, University of California, Los Angeles, Los Angeles, CA and Daniel Meyer, University of Liverpool, Liverpool, UK
Publication: Mathematical Surveys and Monographs
Publication Year:
2017; Volume 225
ISBNs: 978-0-8218-7554-4 (print); 978-1-4704-4252-1 (online)
DOI: https://doi.org/10.1090/surv/225
MathSciNet review: MR3727134
MSC: Primary 37-02; Secondary 30D05, 30L10, 37F10, 37F20
Table of Contents
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Front/Back Matter
Chapters
- Introduction
- Thurston maps
- Lattès 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 Lattès maps
- Outlook and open problems
- Appendix A