Renormalization and 3-Manifolds Which Fiber over the Circle
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle.


Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.

1121677806
Renormalization and 3-Manifolds Which Fiber over the Circle
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle.


Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.

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Renormalization and 3-Manifolds Which Fiber over the Circle

Renormalization and 3-Manifolds Which Fiber over the Circle

by Curtis T. McMullen
Renormalization and 3-Manifolds Which Fiber over the Circle

Renormalization and 3-Manifolds Which Fiber over the Circle

by Curtis T. McMullen

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Overview

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle.


Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.


Product Details

ISBN-13: 9780691011530
Publisher: Princeton University Press
Publication date: 07/28/1996
Series: Annals of Mathematics Studies , #142
Edition description: New Edition
Pages: 253
Product dimensions: 7.75(w) x 10.00(h) x (d)

About the Author

Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.

Table of Contents

1Introduction1
2Rigidity of hyperbolic manifolds11
3Three-manifolds which fiber over the circle41
4Quadratic maps and renormalization75
5Towers95
6Rigidity of towers105
7Fixed points of renormalization119
8Asymptotic structure in the Julia set135
9Geometric limits in dynamics151
10Conclusion175
Appendix A. Quasiconformal maps and flows183
Appendix B. Visual extension205
Bibliography241
Index251
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