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

• Autore: McMullen Curtis T.
• Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 1996; ©1996
• Descrizione fisica: 1 online resource (264 p.)
• Disciplina: 514/.3
• Soggetto topico: Three-manifolds (Topology); Differentiable dynamical systems
• Soggetto non controllato: Algebraic topology; Analytic continuation; Automorphism; Beltrami equation; Bifurcation theory; Boundary (topology); Cantor set; Circular symmetry; Combinatorics; Compact space; Complex conjugate; Complex manifold; Complex number; Complex plane; Conformal geometry; Conformal map; Conjugacy class; Convex hull; Covering space; Deformation theory; Degeneracy (mathematics); Dimension (vector space); Disk (mathematics); Dynamical system; Eigenvalues and eigenvectors; Factorization; Fiber bundle; Fuchsian group; Fundamental domain; Fundamental group; Fundamental solution; G-module; Geodesic; Geometry; Harmonic analysis; Hausdorff dimension; Homeomorphism; Homotopy; Hyperbolic 3-manifold; Hyperbolic geometry; Hyperbolic manifold; Hyperbolic space; Hypersurface; Infimum and supremum; Injective function; Intersection (set theory); Invariant subspace; Isometry; Julia set; Kleinian group; Laplace's equation; Lebesgue measure; Lie algebra; Limit point; Limit set; Linear map; Mandelbrot set; Manifold; Mapping class group; Measure (mathematics); Moduli (physics); Moduli space; Modulus of continuity; Möbius transformation; N-sphere; Newton's method; Permutation; Point at infinity; Polynomial; Quadratic function; Quasi-isometry; Quasiconformal mapping; Quasisymmetric function; Quotient space (topology); Radon–Nikodym theorem; Renormalization; Representation of a Lie group; Representation theory; Riemann sphere; Riemann surface; Riemannian manifold; Schwarz lemma; Simply connected space; Special case; Submanifold; Subsequence; Support (mathematics); Tangent space; Teichmüller space; Theorem; Topology of uniform convergence; Topology; Trace (linear algebra); Transversal (geometry); Transversality (mathematics); Triangle inequality; Unit disk; Unit sphere; Upper and lower bounds; Vector field
• 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.
• Titolo autorizzato: Renormalization and 3-manifolds which fiber over the circle
• ISBN: 0-691-01154-0; 1-4008-6517-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910786510603321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 142.