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Curtis T. McMullen has written 3 work(s)
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Cover for 9780691011547 Cover for 9780691011530 Cover for 9780691029825 Cover for 9780691029818 Cover for 9780898381641
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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.

Hardcover:

9780691011547 | Princeton Univ Pr, July 1, 1996, cover price $95.00 | About this edition: Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade.

Paperback:

9780691011530 | Princeton Univ Pr, July 8, 1996, cover price $82.50

cover image for 9780691029825
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Hardcover:

9780691029825 | Princeton Univ Pr, December 1, 1994, cover price $87.50

Paperback:

9780691029818 | Princeton Univ Pr, November 29, 1994, cover price $75.00 | About this edition: Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.

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