Renormalization and 3-manifolds which fiber over the circle

Author(s)

• McMullen, Curtis Tracy

Bibliographic Information

Renormalization and 3-manifolds which fiber over the circle

by Curtis T. McMullen

（Annals of mathematics studies, no. 142）

Princeton University Press, 1996

• : cl : alk. paper
• : pbk : alk. paper

Note

Includes bibliographical references (p. 241-249) and index

Description and Table of Contents

Volume

: pbk : alk. paper ISBN 9780691011530

Description

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.

Table of Contents

1Introduction12Rigidity of hyperbolic manifolds113Three-manifolds which fiber over the circle414Quadratic maps and renormalization755Towers956Rigidity of towers1057Fixed points of renormalization1198Asymptotic structure in the Julia set1359Geometric limits in dynamics15110Conclusion175Appendix A. Quasiconformal maps and flows183Appendix B. Visual extension205Bibliography241Index251

Volume

: cl : alk. paper ISBN 9780691011547

Description

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.

by "Nielsen BookData"

Details

• NCID: BA28282354
• ISBN:
  • 0691011540
  • 0691011532
• LCCN: 96019081
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Princeton, NJ
• Pages/Volumes: vii, 253 p.
• Size: 25 cm
• Classification:
  • LCC : QA613
  • DC20 : 514/.3
  • NDC8 : 415.2
• Subject Headings:
  • LCSH : Three-manifolds (Topology)
  • LCSH : Differentiable dynamical systems
• Parent Bibliography ID:
  • BA00300336