Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Complex Dynamics and Renormalization (AM-135), Volume 135
Curtis T. McMullen
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Markov partition, Renormalization, Riemann sphere, Moduli (physics), Riemann mapping theorem, Quotient space (topology), Ergodic theory, Uniformization, Complex torus, Hausdorff dimension, Quadratic function, Polynomial, Dihedral group, Point at infinity, Julia set, Limit point, Quasi-isometry, Measure (mathematics), Automorphism, Covering space, Rigidity theory (physics), Analytic function, Open set, Mathematical induction, Uniformization theorem, Special case, Endomorphism, Removable singularity, Euler characteristic, Scientific notation, Geometric function theory, Diagram (category theory), Mandelbrot set, Riemann surface, Monic polynomial, Montel's theorem, Permutation, Equivalence class, Disk (mathematics), Periodic point, Manifold, Quasiconformal mapping, Linear map, Maxima and minima, Pole (complex analysis), Combinatorics, Tangent space, Quadratic differential, Conformal geometry, Holomorphic function, Hyperbolic geometry, Conjecture, Coefficient, Orbifold, Injective function, Subsequence, Dimension (vector space), Complex manifold, Theorem, Symbolic dynamics, Scalar (physics), Schwarz lemma, Complex plane, Cyclic group, Möbius transformation, Unit disk, Homology (mathematics), Kleinian group, Degeneracy (mathematics), Differential geometry of surfaces