Renormalization and 3-Manifolds Which Fiber over the Circle

Häftad, Engelska, 1996

Av Curtis T. McMullen, Curtis T. Mcmullen

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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

Utgivningsdatum1996-07-28
Mått197 x 254 x 14 mm
Vikt340 g
FormatHäftad
SpråkEngelska
SerieAnnals of Mathematics Studies
Antal sidor253
FörlagPrinceton University Press
ISBN9780691011530

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

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