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OverviewMany 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. Full Product DetailsAuthor: Curtis T. McMullenPublisher: Princeton University Press Imprint: Princeton University Press Volume: 153 Dimensions: Width: 19.70cm , Height: 2.20cm , Length: 25.40cm Weight: 0.567kg ISBN: 9780691011547ISBN 10: 0691011540 Pages: 253 Publication Date: 11 August 1996 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Out of Print Availability: Out of stock  Language: English Table of ContentsReviewsA 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. Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians Author InformationCurtis T. McMullen is Professor of Mathematics at the University of California, Berkeley. Tab Content 6Author Website:Countries AvailableAll regions |
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