Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 / / Curtis T. McMullen.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: McMullen, Curtis T.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©1996
• Year of Publication: 2014
• Language: English
• Series: Annals of Mathematics Studies ; 142
• Physical Description: 1 online resource (253 p.)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400865178; 9783110494914; 9783110442496
• DOI: 10.1515/9781400865178
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Curtis T. McMullen.

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.