Renormalization and 3-Manifolds Which Fiber over the Circle

Häftad, Engelska, 1996

Del i serien Annals of Mathematics Studies

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1996-07-28
Mått:197 x 254 x 14 mm
Vikt:340 g
Format:Häftad
Språk:Engelska
Serie:Annals of Mathematics Studies
Antal sidor:253
Förlag:Princeton University Press
ISBN:9780691011530

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Tillämpad matematik inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

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

Recensioner i media

Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "A comprehensive study of a theory which brings into parallel two recent and very deep theorems, involving geometry and dynamics. These are Thurston's theorem on the existence of hyperbolic metrics on three-manifolds which fiber over the circle with pseudo-Anosov monodromy, and Sullivan's theorem on the convergence of the renormalization map for real quadratic mappings... The book is very dense in results and the style is superb."--Mathematical Reviews

Innehållsförteckning

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