Renormalization and 3-manifolds which fiber over the circle / by Curtis T. McMullen.

Format:

Book

Author/Creator:

McMullen, Curtis T., author.

Series:

Annals of mathematics studies ; Number 142.

Annals of Mathematics Studies ; Number 142

Language:

English

Subjects (All):

Three-manifolds (Topology).

Differentiable dynamical systems.

Physical Description:

1 online resource (264 p.)

Edition:

1st ed.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1996.

Language Note:

English

Summary:

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.

Contents:

Front matter

Contents

1 Introduction

2 Rigidity of hyperbolic manifolds

3 Three-manifolds which fiber over the circle

4 Quadratic maps and renormalization

5 Towers

6 Rigidity of towers

7 Fixed points of renormalization

8 Asymptotic structure in the Julia set

9 Geometric limits in dynamics

10 Conclusion

Appendix A. Quasiconformal maps and flows

Appendix B Visual extension

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-691-01154-0

1-4008-6517-4

OCLC:

887499131