Description
Book SynopsisGives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity.
Trade ReviewCurtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "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 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."--Mathematical Reviews
Table of Contents1Introduction12Rigidity of hyperbolic manifolds113Three-manifolds which fiber over the circle414Quadratic maps and renormalization755Towers956Rigidity of towers1057Fixed points of renormalization1198Asymptotic structure in the Julia set1359Geometric limits in dynamics15110Conclusion175Appendix A. Quasiconformal maps and flows183Appendix B. Visual extension205Bibliography241Index251
