LEADER 03061nam 2200589 450 001 9910812438203321 005 20180613001308.0 010 $a1-4704-0497-4 035 $a(CKB)3360000000465075 035 $a(EBL)3114158 035 $a(SSID)ssj0000889088 035 $a(PQKBManifestationID)11452880 035 $a(PQKBTitleCode)TC0000889088 035 $a(PQKBWorkID)10866182 035 $a(PQKB)10657961 035 $a(MiAaPQ)EBC3114158 035 $a(RPAM)15004286 035 $a(PPN)195417801 035 $a(EXLCZ)993360000000465075 100 $a20070912h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNewton's method applied to two quadratic equations in C[superscript 2] viewed as a global dynamical system /$fJohn H. Hubbard, Peter Papadopol 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (160 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 891 300 $aDescription based upon print version of record. 311 $a0-8218-4056-8 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""Chapter 2 Invariant 3-manifolds associated to invariant circles""""2.1. The circles in the invariant lines""; ""2.2. Periodic cycles on invariant circles""; ""2.3. Unstable manifolds at infinity""; ""2.4. The invariant manifolds of circles""; ""2.5. The extension of I?? and the origin of ""bubbles""""; ""Chapter 3 The behavior at infinity when a = b = 0""; ""3.1. The primitive space""; ""3.2. Newton's method and the primitive space""; ""Chapter 4 The Farey blow-up""; ""4.1. Definition of the Farey blow-up""; ""4.2. Naturality of the Farey blow-up"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 891. 606 $aNewton-Raphson method 606 $aEquations, Quadratic 606 $aDifferentiable dynamical systems 615 0$aNewton-Raphson method. 615 0$aEquations, Quadratic. 615 0$aDifferentiable dynamical systems. 676 $a515/.39 700 $aHubbard$b John H$g(John Hamal),$f1945 or 1946-$021456 702 $aPapadopol$b Peter$f1931- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812438203321 996 $aNewton's method applied to two quadratic equations in C viewed as a global dynamical system$94110271 997 $aUNINA