Matrix
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*serious mathematics, written with the reader in mind*

Surface Homeomorphisms and Rational Functions

John H. Hubbard

ISBN 9781943863006

262 pages

hardcover, smythe-sewn binding

108 color illustrations

Table of contents (in html)

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See also:

Volume 1: Teichmüller theory

Volume 3: Manifolds that Fiber over the Circle (not yet published)

Volume 4: Hyperbolization of Haken Manifolds (not yet published)

Chapter 8 The classification of homeomorphisms of surfaces

8.1 The classification theorem

8.2 Periodic and reducible homeomorphisms

8.3 Pseudo-Anosov homeomorphisms

8.4 Proof of the classification theorem

8.5 The structure in the reducible case

Chapter 9 Dynamics of polynomials

9.1 Julia sets

9.2 Fixed points

9.3 Green's functions, Böttcher coordinates

9.4 Extending f_{0} to S^{1}

9.5 External rays at rational angles land

Chapter 10 Rational functions

10.1 Introduction

10.1 Thurston mappings

10.2 Thurston maps associated to spiders

10.3 Thurston obstructions for spider maps and Levy cycles

10.4 Julia sets of quadratic polynomials with superattracting cycles

10.5 Parameter spaces for quadratic polynomials

10.6 The Thurston pullback mapping

10.7 The derivative and coderivative of Thurston pullback mapping

10.8 The necessity of the eigenvalue criterion

10.9 Convergence in moduli spaces implies convergence in Teichmüller space

10.10 Asymptotic geometry of Riemann surfaces

10.11 Sufficiency of the eigenvalue criterion

Appendix C1 The Perron-Frobenius theorem

Appendix C2 The Alexander trick

Appendix C3 Homotopy implies isotopy

Appendix C4 The mapping class group and outer automorphisms

Appendix C5 Totally real stretch factors

Appendix C6 Irrationally indifferent fixed points

Appendix C7 Examples of Thurston pullback maps

Appendix C8 Branched maps with nonhyperbolic orbifolds

Appendix C9 The Sullivan dictionary

Bibliography

Index

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