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.
Rezensionen / Stimmen
"Curtis 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 *
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Maße
Höhe: 254 mm
Breite: 197 mm
Gewicht
ISBN-13
978-0-691-01154-7 (9780691011547)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.
