03061nam 2200589 450 991081243820332120180613001308.01-4704-0497-4(CKB)3360000000465075(EBL)3114158(SSID)ssj0000889088(PQKBManifestationID)11452880(PQKBTitleCode)TC0000889088(PQKBWorkID)10866182(PQKB)10657961(MiAaPQ)EBC3114158(RPAM)15004286(PPN)195417801(EXLCZ)99336000000046507520070912h20082008 uy| 0engur|n|---|||||txtccrNewton's method applied to two quadratic equations in C[superscript 2] viewed as a global dynamical system /John H. Hubbard, Peter PapadopolProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (160 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 891Description based upon print version of record.0-8218-4056-8 Includes bibliographical references.""Table of Contents""; ""Chapter 0 Introduction""; ""1. Introduction""; ""2. Outline of paper""; ""3. Acknowledgements""; ""4. A computer tour of Newton's method""; ""5. Some open questions""; ""Chapter 1 Fundamental properties of Newton maps""; ""1.1. Generalities about Newton's method""; ""1.2. The intersection of graphs""; ""1.3. The Russakovskii-Shiffman measure""; ""1.4. Invariant currents""; ""1.5. The intersection of conies""; ""1.6. Degenerate cases""; ""1.7. The one-variable rational functions associated to the roots""""Chapter 2 Invariant 3-manifolds associated to invariant circles""""2.1. The circles in the invariant lines""; ""2.2. Periodic cycles on invariant circles""; ""2.3. Unstable manifolds at infinity""; ""2.4. The invariant manifolds of circles""; ""2.5. The extension of Î? and the origin of ""bubbles""""; ""Chapter 3 The behavior at infinity when a = b = 0""; ""3.1. The primitive space""; ""3.2. Newton's method and the primitive space""; ""Chapter 4 The Farey blow-up""; ""4.1. Definition of the Farey blow-up""; ""4.2. Naturality of the Farey blow-up""Memoirs of the American Mathematical Society ;no. 891.Newton-Raphson methodEquations, QuadraticDifferentiable dynamical systemsNewton-Raphson method.Equations, Quadratic.Differentiable dynamical systems.515/.39Hubbard John H(John Hamal),1945 or 1946-21456Papadopol Peter1931-MiAaPQMiAaPQMiAaPQBOOK9910812438203321Newton's method applied to two quadratic equations in C viewed as a global dynamical system4110271UNINA