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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.

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Book Details

ISBN: 9780691011530
ISBN-10: 0691011532
Format: Paperback
(229mm x 152mm x 14mm)
Pages: 253
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 8-Jul-1996
Country of Publication: United States

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