TY  - BOOK
AU  - Beardon,Alan F
TI  - Iteration of rational functions: complex analytic dynamical systems 
T2  - Graduate texts in mathematics
SN  - 0387951512
AV  - QA297.8 .B43 2000
PY  - 2000///]
CY  - New York
PB  - Springer
KW  - Iterative methods (Mathematics)
KW  - Mappings (Mathematics)
N1  - Includes bibliographical references (pages [273]-277) and indexes; Table Of Contents; Preface; Prerequisites; Examples; Introduction; Iteration of Mobius Transformations; Iteration of z ↦ z2; Tchebychev Polynomials; Iteration of z andmap z2-1; Iteration of z andmap z2 + c; Iteration of z andmap z + 1/z; Iteration of z andmap 2z - 1/z; Newton's Approximation; General Remarks; Rational Maps; The Extended Complex Plane; Rational Maps; The Lipschitz Condition; Conjugacy; Valency; Fixed Points; Critical Points; A Topology on the Rational Functions; The Fator and Julia Sets; The Fatou and Julia Sets; Completely Invariant Sets; Normal Families and Equicontinuity; The Hyperbolic Metric; Properties of the Julia Set; Exceptional Points; Properties of the Julia Set; Rational Maps with Empty Fatou Set; Elliptic Functions; The Structure of the Fatou Set; The Toplogy of the Sphere; Completely Invariant Components of the Fatou Set; The Euler Characteristic; The Riemann-Hurwitz Formula for Covering Maps; Maps Between Components of the Fatou Set; The Number of Components of the Fatou Set; Components of the Julia Set; Periodic Points; The Classification of Periodic Points; The Ecistence of Periodic Points; (Super) Atracting Cycles; Repelling Cycles; Rationally Indifferent Cycles; Irrationally Indifferent Cycles in F; Irrationally Indifferent Cycles in J; The Proof of the Existence of Periodic Points; The Julia Set and Periodic Points; Local Conjugacy; Infinite Products; The Universal Covering Surface; Forward Invariant Components; The Five Possibilities; Limit Functions; Parabolic Domains; Siegel Discs and Herman Rings; Connectivity of Invariant Components; The No Wandering Domains Theorem; The No Wandering Domains Theorem; A Preliminary Result; Conformal Structures; Quasiconformal Conjugates of Rational Maps; Boundary Values of Conjugate Maps; The Proof of Theorem 8.1.2; Critical Points; Introductory Remarks; The Normality of Inverse Maps; Critical Points and Periodic Domains; Applications; The Fatou Set of a Polynomial; The Number of Non-Repelling Cycles; Expanding Maps; Julia Sets as Cantor Sets; Julia Sets as Jordan Curves; The Mandelbrot Set; Hausdorff Dimension; Hausdorff Dimension; Computing Dimensions; The Dimension of Julia Sets; Examples; Smooth Julia Sets; Dendrites; Components of F of Infinite Connectivity; F with Infinitely Connected and Simply Connected Components; J with Infinitely Many Non-Degenerate Components; F of Infinite Connectivity with Critical Points in J; A Finitely Connected Component of F; J Is a Cantor Set of Circles; The Function (z - 2)2/z2; References; Index of Examples; Index
ER  -