TY  - BOOK
AU  - Graczyk,Jacek
AU  - Świa̧tek,Grzegorz
TI  - The real Fatou conjecture
T2  - Annals of mathematics studies
SN  - 9781400865185
AV  - QA614.58 .G73 1998eb
U1  - 516.362 23
PY  - 1998///
CY  - Princeton, N.J.
PB  - Princeton University Press
KW  - Geodesics (Mathematics)
KW  - Mappings (Mathematics)
KW  - Polynomials
KW  - Mathematik
KW  - Géodésiques (Mathématiques)
KW  - Applications (Mathématiques)
KW  - Polynômes
KW  - MATHEMATICS
KW  - Geometry
KW  - General
KW  - bisacsh
KW  - Complex Analysis
KW  - fast
KW  - Absolute value
KW  - Affine transformation
KW  - Algebraic function
KW  - Analytic continuation
KW  - Analytic function
KW  - Arithmetic
KW  - Automorphism
KW  - Big O notation
KW  - Bounded set (topological vector space)
KW  - C0
KW  - Calculation
KW  - Canonical map
KW  - Change of variables
KW  - Chebyshev polynomials
KW  - Combinatorics
KW  - Commutative property
KW  - Complex number
KW  - Complex plane
KW  - Complex quadratic polynomial
KW  - Conformal map
KW  - Conjecture
KW  - Conjugacy class
KW  - Conjugate points
KW  - Connected component (graph theory)
KW  - Connected space
KW  - Continuous function
KW  - Corollary
KW  - Covering space
KW  - Critical point (mathematics)
KW  - Dense set
KW  - Derivative
KW  - Diffeomorphism
KW  - Dimension
KW  - Disjoint sets
KW  - Disjoint union
KW  - Disk (mathematics)
KW  - Equicontinuity
KW  - Estimation
KW  - Existential quantification
KW  - Fibonacci
KW  - Functional equation
KW  - Fundamental domain
KW  - Generalization
KW  - Great-circle distance
KW  - Hausdorff distance
KW  - Holomorphic function
KW  - Homeomorphism
KW  - Homotopy
KW  - Hyperbolic function
KW  - Imaginary number
KW  - Implicit function theorem
KW  - Injective function
KW  - Integer
KW  - Intermediate value theorem
KW  - Interval (mathematics)
KW  - Inverse function
KW  - Irreducible polynomial
KW  - Iteration
KW  - Jordan curve theorem
KW  - Julia set
KW  - Limit of a sequence
KW  - Linear map
KW  - Local diffeomorphism
KW  - Mathematical induction
KW  - Mathematical proof
KW  - Maxima and minima
KW  - Meromorphic function
KW  - Moduli (physics)
KW  - Monomial
KW  - Monotonic function
KW  - Natural number
KW  - Neighbourhood (mathematics)
KW  - Open set
KW  - Parameter
KW  - Periodic function
KW  - Periodic point
KW  - Phase space
KW  - Point at infinity
KW  - Polynomial
KW  - Projection (mathematics)
KW  - Quadratic function
KW  - Quadratic
KW  - Quasiconformal mapping
KW  - Renormalization
KW  - Riemann sphere
KW  - Riemann surface
KW  - Schwarzian derivative
KW  - Scientific notation
KW  - Subsequence
KW  - Theorem
KW  - Theory
KW  - Topological conjugacy
KW  - Topological entropy
KW  - Topology
KW  - Union (set theory)
KW  - Unit circle
KW  - Unit disk
KW  - Upper and lower bounds
KW  - Upper half-plane
KW  - Z0
N1  - Includes bibliographical references and index; Frontmatter --; Contents --; Chapter 1. Review of Concepts --; Chapter 2. Quasiconformal Gluing --; Chapter 3. Polynomial-Like Property --; Chapter 4. Linear Growth of Moduli --; Chapter 5. Quasi conformal Techniques --; Bibliography --; Index
N2  - In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=818439
ER  -