Renormalization and 3-Manifolds Which Fiber over the Circle

Erscheinungsjahr 1996
ISBN: 978-0-691-01153-0
Verlag: Princeton University Press

Buch, Englisch, Band (AM-142), 253 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 388 g

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

McMullen, Curtis T.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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