


Renormalization and 3Manifolds Which Fiber over the Circle (AM142) 
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 fixedpoints 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 quadraticlike maps, and leads to a quantitative proof of convergence of renormalization. "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 threemanifolds which fiber over the circle with pseudoAnosov 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 Another Princeton book authored or coauthored by Curtis T. McMullen: Series:
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