06680nam 2201885 450 991081680450332120230421030941.00-691-00257-61-4008-6518-210.1515/9781400865185(CKB)3710000000221858(EBL)1756204(OCoLC)887499708(SSID)ssj0001333670(PQKBManifestationID)12618247(PQKBTitleCode)TC0001333670(PQKBWorkID)11394032(PQKB)11541986(MiAaPQ)EBC1756204(DE-B1597)447948(OCoLC)922696192(DE-B1597)9781400865185(Au-PeEL)EBL1756204(CaPaEBR)ebr10907682(CaONFJC)MIL636773(EXLCZ)99371000000022185820140822h19981998 uy 0engur|nu---|u||utxtccrThe real Fatou conjecture /by Jacek Graczyk and Grzegorz SwiatekPrinceton, New Jersey :Princeton University Press,1998.{copy}19981 online resource (158 p.)Annals of Mathematics Studies ;Number 144Description based upon print version of record.1-322-05522-X 0-691-00258-4 Includes bibliographical references and index.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 --IndexIn 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.Annals of mathematics studies ;Number 144.Geodesics (Mathematics)PolynomialsMappings (Mathematics)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.Geodesics (Mathematics)Polynomials.Mappings (Mathematics)516.3/62Graczyk Jacek66776Swiatek Grzegorz1964-MiAaPQMiAaPQMiAaPQBOOK9910816804503321Real Fatou conjecture1501746UNINA