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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

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Table of Contents

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Front/Back Matter

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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