Cantitate/Preț
Produs
Total produse
Vezi coșul
Iteration of Rational Functions: Complex Analytic Dynamical Systems de Alan F. Beardon

Iteration of Rational Functions: Complex Analytic Dynamical Systems: Graduate Texts in Mathematics, cartea 132

Autor Alan F. Beardon
en Limba Engleză Paperback – 27 sep 2000
This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before. The theory of of dynamical systems and chaos has recently undergone a rapid growth in popularity, in part due to the spectacular computer graphics of Julia sets, fractals, and the Mandelbrot set. This text focuses on the specialized area of complex analytic dynamics, a subject that dates back to 1916 and is currently a very active area in mathematics.
Citește tot Restrânge

Din seria Graduate Texts in Mathematics

  • Problems in Analytic Number Theory
    Preț: 40287 lei
  • Functions of One Complex Variable I
    Preț: 36166 lei
  • 17% Complex Analysis
    Preț: 39896 lei
  • Applications of Lie Groups to Differential Equations
    Preț: 35582 lei
  • Advanced Linear Algebra
    Preț: 44205 lei
  • Real and Functional Analysis
    Preț: 38025 lei
  • Commutative Algebra: with a View Toward Algebraic Geometry
    Preț: 28986 lei
  • 17% Advanced Topics in the Arithmetic of Elliptic Curves
    Preț: 36579 lei
  • 17% Classical Descriptive Set Theory
    Preț: 35944 lei
  • Groups and Representations
    Preț: 45063 lei
  • Graph Theory
    Preț: 38097 lei
  • An Introduction to Knot Theory
    Preț: 43130 lei
  • 18% Introduction to Riemannian Manifolds
    Preț: 34031 lei
  • 13% Algebra
    Preț: 36138 lei
  • 13% Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
    Preț: 35574 lei
  • 17% A First Course in Modular Forms
    Preț: 35957 lei
  • Ergodic Theory: with a view towards Number Theory
    Preț: 48466 lei
  • 20% Calculus Without Derivatives
    Preț: 57125 lei
  • 15% Quantum Theory for Mathematicians
    Preț: 53095 lei
  • Integer Programming
    Preț: 48447 lei
  • 15% Homotopical Topology
    Preț: 35438 lei
  • Brownian Motion, Martingales, and Stochastic Calculus
    Preț: 39629 lei
  • 13% Differential Geometry: Connections, Curvature, and Characteristic Classes
    Preț: 42996 lei
  • 17% Intersection Homology & Perverse Sheaves: with Applications to Singularities
    Preț: 36359 lei
  • 18% Measure, Integration & Real Analysis
    Preț: 28094 lei
  • 17% Basic Representation Theory of Algebras
    Preț: 36447 lei
  • 17% Spectral Theory: Basic Concepts and Applications
    Preț: 36647 lei
  • 17% Explorations in Complex Functions
    Preț: 36606 lei
  • Quaternion Algebras
    Preț: 24758 lei
  • 17% Lessons in Enumerative Combinatorics
    Preț: 36770 lei
  • 13% Mathematical Logic
    Preț: 35937 lei
  • 17% Partial Differential Equations: An Introduction to Analytical and Numerical Methods
    Preț: 39877 lei
  • 17% Measure Theory, Probability, and Stochastic Processes
    Preț: 39850 lei
  • 17% Drinfeld Modules
    Preț: 49622 lei
  • 13% An Introduction to Automorphic Representations: With a view toward trace formulae
    Preț: 36437 lei
  • 20% Several Complex Variables
    Preț: 44972 lei
  • Categories for the Working Mathematician
    Preț: 38307 lei
  • Algebraic Geometry
    Preț: 36479 lei
  • 17% p-adic Numbers, p-adic Analysis, and Zeta-Functions
    Preț: 42727 lei
  • Algebra
    Preț: 35719 lei
  • An Introduction to Ergodic Theory
    Preț: 40499 lei
  • 17% Lectures on Riemann Surfaces
    Preț: 39586 lei
  • Differential Forms in Algebraic Topology
    Preț: 37619 lei
  • 13% A Classical Introduction to Modern Number Theory
    Preț: 41703 lei
  • 15% Representation Theory: A First Course
    Preț: 58646 lei
  • 15% Theory of Complex Functions
    Preț: 58231 lei
  • Mathematical Methods of Classical Mechanics
    Preț: 38658 lei

Preț: 48517 lei

Preț vechi: 57079 lei
-15% Nou

Puncte Express: 728
Preț estimativ în valută:
9284€ • 9765$ • 7758£

Carte tipărită la comandă

Livrare economică 08-22 ianuarie 25

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă
Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9780387951515
ISBN-10: 0387951512
Pagini: 280
Ilustrații: XVI, 280 p. 1 illus.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.42 kg
Ediția:Softcover reprint of the original 1st ed. 1991
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

1 Examples.- 1.1. Introduction.- 1.2. Iteration of Möbius Transformations.- 1.3. Iteration of z ? z2.- 1.4. Tchebychev Polynomials.- 1.5. Iteration of z ? z2 ? 1.- 1.6. Iteration of z ? z2 + c.- 1.7. Iteration of z ? z + 1/z.- 1.8. Iteration of z ? 2z ? 1/z.- 1.9. Newton’s Approximation.- 1.10. General Remarks.- 2 Rational Maps.- 2.1. The Extended Complex Plane.- 2.2. Rational Maps.- 2.3. The Lipschitz Condition.- 2.4. Conjugacy.- 2.5. Valency.- 2.6. Fixed Points.- 2.7. Critical Points.- 2.8. A Topology on the Rational Functions.- 3 The Fatou and Julia Sets.- 3.1. The Fatou and Julia Sets.- 3.2. Completely Invariant Sets.- 3.3. Normal Families and Equicontinuity.- Appendix I. The Hyperbolic Metric.- 4 Properties of the Julia Set.- 4.1. Exceptional Points.- 4.2. Properties of the Julia Set.- 4.3. Rational Maps with Empty Fatou Set.- Appendix II. Elliptic Functions.- 5 The Structure of the Fatou Set.- 5.1. The Topology of the Sphere.- 5.2. Completely Invariant Components of the Fatou Set.- 5.3. The Euler Characteristic.- 5.4. The Riemann-Hurwitz Formula for Covering Maps.- 5.5. Maps Between Components of the Fatou Set.- 5.6. The Number of Components of the Fatou Set.- 5.7. Components of the Julia Set.- 6 Periodic Points.- 6.1. The Classification of Periodic Points.- 6.2. The Existence of Periodic Points.- 6.3. (Super) Attracting Cycles.- 6.4. Repelling Cycles.- 6.5. Rationally Indifferent Cycles.- 6.6. Irrationally Indifferent Cycles in F.- 6.7. Irrationally Indifferent Cycles in J.- 6.8. The Proof of the Existence of Periodic Points.- 6.9. The Julia Set and Periodic Points.- 6.10. Local Conjugacy.- Appendix III. Infinite Products.- Appendix IV. The Universal Covering Surface.- 7 Forward Invariant Components.- 7.1. The Five Possibilities.- 7.2. LimitFunctions.- 7.3. Parabolic Domains.- 7.4. Siegel Discs and Herman Rings.- 7.5. Connectivity of Invariant Components.- 8 The No Wandering Domains Theorem.- 8.1. The No Wandering Domains Theorem.- 8.2. A Preliminary Result.- 8.3. Conformal Structures.- 8.4. Quasiconformal Conjugates of Rational Maps.- 8.5. Boundary Values of Conjugate Maps.- 8.6. The Proof of Theorem 8.1.2.- 9 Critical Points.- 9.1. Introductory Remarks.- 9.2. The Normality of Inverse Maps.- 9.3. Critical Points and Periodic Domains.- 9.4. Applications.- 9.5. The Fatou Set of a Polynomial.- 9.6. The Number of Non-Repelling Cycles.- 9.7. Expanding Maps.- 9.8. Julia Sets as Cantor Sets.- 9.9. Julia Sets as Jordan Curves.- 9.10. The Mandelbrot Set.- 10 Hausdorff Dimension.- 10.1. Hausdorff Dimension.- 10.2. Computing Dimensions.- 10.3. The Dimension of Julia Sets.- 11 Examples.- 11.1. Smooth Julia Sets.- 11.2. Dendrites.- 11.3. Components of F of Infinite Connectivity.- 11.4. F with Infinitely Connected and Simply Connected Components.- 11.5. J with Infinitely Many Non-Degenerate Components.- 11.6. F of Infinite Connectivity with Critical Points in J.- 11.7. A Finitely Connected Component of F.- 11.8. J Is a Cantor Set of Circles.- 11.9. The Function (z ? 2)2/z2.- References.- Index of Examples.

Recenzii

A.F. Beardon
Iteration of Rational Functions
Complex Analytic Dynamical Systems
"This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before."—ZENTRALBLATT MATH