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The real Fatou conjecture / / by Jacek Graczyk and Grzegorz Swiatek



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Autore: Graczyk Jacek Visualizza persona
Titolo: The real Fatou conjecture / / by Jacek Graczyk and Grzegorz Swiatek Visualizza cluster
Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 1998
{copy}1998
Descrizione fisica: 1 online resource (158 p.)
Disciplina: 516.3/62
Soggetto topico: Geodesics (Mathematics)
Polynomials
Mappings (Mathematics)
Soggetto non controllato: Absolute value
Affine transformation
Algebraic function
Analytic continuation
Analytic function
Arithmetic
Automorphism
Big O notation
Bounded set (topological vector space)
C0
Calculation
Canonical map
Change of variables
Chebyshev polynomials
Combinatorics
Commutative property
Complex number
Complex plane
Complex quadratic polynomial
Conformal map
Conjecture
Conjugacy class
Conjugate points
Connected component (graph theory)
Connected space
Continuous function
Corollary
Covering space
Critical point (mathematics)
Dense set
Derivative
Diffeomorphism
Dimension
Disjoint sets
Disjoint union
Disk (mathematics)
Equicontinuity
Estimation
Existential quantification
Fibonacci
Functional equation
Fundamental domain
Generalization
Great-circle distance
Hausdorff distance
Holomorphic function
Homeomorphism
Homotopy
Hyperbolic function
Imaginary number
Implicit function theorem
Injective function
Integer
Intermediate value theorem
Interval (mathematics)
Inverse function
Irreducible polynomial
Iteration
Jordan curve theorem
Julia set
Limit of a sequence
Linear map
Local diffeomorphism
Mathematical induction
Mathematical proof
Maxima and minima
Meromorphic function
Moduli (physics)
Monomial
Monotonic function
Natural number
Neighbourhood (mathematics)
Open set
Parameter
Periodic function
Periodic point
Phase space
Point at infinity
Polynomial
Projection (mathematics)
Quadratic function
Quadratic
Quasiconformal mapping
Renormalization
Riemann sphere
Riemann surface
Schwarzian derivative
Scientific notation
Subsequence
Theorem
Theory
Topological conjugacy
Topological entropy
Topology
Union (set theory)
Unit circle
Unit disk
Upper and lower bounds
Upper half-plane
Z0
Persona (resp. second.): SwiatekGrzegorz <1964->
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- 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
Sommario/riassunto: 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.
Titolo autorizzato: Real Fatou conjecture  Visualizza cluster
ISBN: 0-691-00257-6
1-4008-6518-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910786510203321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; Number 144.