Renormalization and 3-manifolds which fiber over the circle / / by Curtis T. McMullen

• Record Nr.: UNINA9910786510603321
• Autore: McMullen Curtis T.
• Pubbl/distr/stampa: Princeton, New Jersey : , : Princeton University Press, , 1996; ©1996
• ISBN: 0-691-01154-0; 1-4008-6517-4
• Descrizione fisica: 1 online resource (264 p.)
• Collana: Annals of Mathematics Studies ; ; Number 142
• Disciplina: 514/.3
• Soggetti: Three-manifolds (Topology); Differentiable dynamical systems
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- 1 Introduction -- 2 Rigidity of hyperbolic manifolds -- 3 Three-manifolds which fiber over the circle -- 4 Quadratic maps and renormalization -- 5 Towers -- 6 Rigidity of towers -- 7 Fixed points of renormalization -- 8 Asymptotic structure in the Julia set -- 9 Geometric limits in dynamics -- 10 Conclusion -- Appendix A. Quasiconformal maps and flows -- Appendix B Visual extension -- Bibliography -- Index
• Sommario/riassunto: 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.