Complex Dynamics and Renormalization (AM-135), Volume 135 / / Curtis T. McMullen

• Autore: McMullen Curtis T.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1995
• Descrizione fisica: 1 online resource (229 pages) : illustrations
• Disciplina: 530.1/43/0151
• Soggetto topico: Renormalization (Physics); Polynomials; Dynamics; Mathematical physics
• Soggetto non controllato: Analytic function; Attractor; Automorphism; Bernhard Riemann; Bounded set; Branched covering; Cantor set; Cardioid; Chain rule; Coefficient; Combinatorics; Complex manifold; Complex plane; Complex torus; Conformal geometry; Conformal map; Conjecture; Connected space; Covering space; Cyclic group; Degeneracy (mathematics); Dense set; Diagram (category theory); Diameter; Differential geometry of surfaces; Dihedral group; Dimension (vector space); Dimension; Disjoint sets; Disk (mathematics); Dynamical system; Endomorphism; Equivalence class; Equivalence relation; Ergodic theory; Euler characteristic; Filled Julia set; Geometric function theory; Geometry; Hausdorff dimension; Holomorphic function; Homeomorphism; Homology (mathematics); Hyperbolic geometry; Implicit function theorem; Injective function; Integer matrix; Interval (mathematics); Inverse limit; Julia set; Kleinian group; Limit point; Limit set; Linear map; Mandelbrot set; Manifold; Markov partition; Mathematical induction; Maxima and minima; Measure (mathematics); Moduli (physics); Monic polynomial; Montel's theorem; Möbius transformation; Natural number; Open set; Orbifold; Periodic point; Permutation; Point at infinity; Pole (complex analysis); Polynomial; Proper map; Quadratic differential; Quadratic function; Quadratic; Quasi-isometry; Quasiconformal mapping; Quotient space (topology); Removable singularity; Renormalization; Riemann mapping theorem; Riemann sphere; Riemann surface; Rigidity theory (physics); Scalar (physics); Schwarz lemma; Scientific notation; Special case; Structural stability; Subgroup; Subsequence; Symbolic dynamics; Tangent space; Theorem; Uniformization theorem; Uniformization; Union (set theory); Unit disk; Upper and lower bounds
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index
• Sommario/riassunto: Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.
• Titolo autorizzato: Complex Dynamics and Renormalization (AM-135), Volume 135
• ISBN: 1-4008-8255-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154745403321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 135.