Renormalization and 3-Manifolds Which Fiber Over the Circle
By (author) Curtis T. McMullen
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Renormalization and 3-Manifolds Which Fiber Over the Circle by Curtis T. McMullen
Book DescriptionMany 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.
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Book DetailsISBN: 9780691011530
(229mm x 152mm x 14mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 8-Jul-1996
Country of Publication: United States
Books By Author Curtis T. McMullen
Complex Dynamics and Renormalization, Paperback (November 1994)» View all books by Curtis T. McMullen
Addressing researchers and graduate students in the meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and an introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c.
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