Quasiconformal Surgery in Holomorphic DynamicsCambridge University Press, 23.01.2014 - 416 Seiten Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors begin with the foundations and a general description of surgery techniques before turning their attention to a wide variety of applications. They demonstrate the different types of surgeries that lie behind many important results in holomorphic dynamics, dealing in particular with Julia sets and the Mandelbrot set. Two of these surgeries go beyond the classical realm of quasiconformal surgery and use trans-quasiconformal surgery. Another deals with holomorphic correspondences, a natural generalization of holomorphic maps. The book is ideal for graduate students and researchers requiring a self-contained text including a variety of applications. It particularly emphasises the geometrical ideas behind the proofs, with many helpful illustrations seldom found in the literature. |
Inhalt
Quasiconformal geometry | 7 |
Preliminaries on dynamical systems and actions of Kleinian | 92 |
Introduction to surgery and first occurrences | 147 |
General principles of surgery | 179 |
Soft surgeries | 188 |
Cut and paste surgeries | 218 |
Cut and paste surgeries with sectors | 307 |
Transquasiconformal surgery | 364 |
400 | |
408 | |
Andere Ausgaben - Alle anzeigen
Quasiconformal Surgery in Holomorphic Dynamics Bodil Branner,Núria Fagella,Xavier Buff Eingeschränkte Leseprobe - 2014 |
Häufige Begriffe und Wortgruppen
ˇ ˇ annulus basin of attraction Beltrami coefficient Beltrami form Blaschke products boundary maps bounded complex structure conjugacy connected component connectedness locus construction contains critical point cubic polynomial cycle defined Definition degree denote dilatation domain ellipse exists extends Fatou components Fatou set fig Figure filled Julia set finite fixed point follows Hence Herman ring holomorphic dynamics holomorphic map homeomorphism hybrid equivalent hyperbolic component Integrability Theorem integrating map invariant Jordan curve Kleinian group Lemma Let f linearizing Mandelbrot set map f modulus multiplier neighbourhood obtain orientation preserving parabolic parameter preimages proof Proposition pullback quadratic polynomial quasicircle quasiconformal homeomorphism quasiconformal map quasiconformally conjugate quasiregular map quasisymmetric map rational map Riemann map Riemann surface rigid rotation rotation number rotation ring satisfies Section sectors Siegel disc subset surgery topological unique unit circle unit disc