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100   $a20050627d2006      uy             0
101 0 $aeng
135   $aurcn|||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aDynamics in one complex variable$b[electronic resource] /$fby John Milnor
205   $a3rd ed.
210   $aPrinceton, N.J. $cPrinceton University Press$d2006
215   $a1 online resource (313 p.)
225 1 $aAnnals of mathematics studies ;$vno. 160
300   $aDescription based upon print version of record.
311   $a0-691-12487-6 
311   $a0-691-12488-4 
320   $aIncludes bibliographical references (p. 277-291) and index.
327   $t Frontmatter -- $tTable Of Contents -- $tList of Figures -- $tPreface to the Third Edition -- $tChronological Table -- $tRiemann Surfaces -- $tIterated Holomorphic Maps -- $tLocal Fixed Point Theory -- $tPeriodic Points: Global Theory -- $tStructure of the Fatou Set -- $tUsing the Fatou Set to Study the Julia Set -- $tAppendix A. Theorems from Classical Analysis -- $tAppendix B. Length-Area-Modulus Inequalities -- $tAppendix C. Rotations, Continued Fractions, and Rational Approximation -- $tAppendix D. Two or More Complex Variables -- $tAppendix E. Branched Coverings and Orbifolds -- $tAppendix F. No Wandering Fatou Components -- $tAppendix G. Parameter Spaces -- $tAppendix H. Computer Graphics and Effective Computation -- $tReferences -- $tIndex
330   $aThis volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
410  0$aAnnals of mathematics studies ;$vno. 160.
606   $aFunctions of complex variables
606   $aHolomorphic mappings
606   $aRiemann surfaces
610   $aAbsolute value.
610   $aAddition.
610   $aAlgebraic equation.
610   $aAttractor.
610   $aAutomorphism.
610   $aBeltrami equation.
610   $aBlaschke product.
610   $aBoundary (topology).
610   $aBranched covering.
610   $aCoefficient.
610   $aCompact Riemann surface.
610   $aCompact space.
610   $aComplex analysis.
610   $aComplex number.
610   $aComplex plane.
610   $aComputation.
610   $aConnected component (graph theory).
610   $aConnected space.
610   $aConstant function.
610   $aContinued fraction.
610   $aContinuous function.
610   $aCoordinate system.
610   $aCorollary.
610   $aCovering space.
610   $aCross-ratio.
610   $aDerivative.
610   $aDiagram (category theory).
610   $aDiameter.
610   $aDiffeomorphism.
610   $aDifferentiable manifold.
610   $aDisjoint sets.
610   $aDisjoint union.
610   $aDisk (mathematics).
610   $aDivision by zero.
610   $aEquation.
610   $aEuler characteristic.
610   $aExistential quantification.
610   $aExponential map (Lie theory).
610   $aFundamental group.
610   $aHarmonic function.
610   $aHolomorphic function.
610   $aHomeomorphism.
610   $aHyperbolic geometry.
610   $aInequality (mathematics).
610   $aInteger.
610   $aInverse function.
610   $aIrrational rotation.
610   $aIteration.
610   $aJordan curve theorem.
610   $aJulia set.
610   $aLebesgue measure.
610   $aLecture.
610   $aLimit point.
610   $aLine segment.
610   $aLinear map.
610   $aLinearization.
610   $aMandelbrot set.
610   $aMathematical analysis.
610   $aMaximum modulus principle.
610   $aMetric space.
610   $aMonotonic function.
610   $aMontel's theorem.
610   $aNormal family.
610   $aOpen set.
610   $aOrbifold.
610   $aParameter space.
610   $aParameter.
610   $aPeriodic point.
610   $aPoint at infinity.
610   $aPolynomial.
610   $aPower series.
610   $aProper map.
610   $aQuadratic function.
610   $aRational approximation.
610   $aRational function.
610   $aRational number.
610   $aReal number.
610   $aRiemann sphere.
610   $aRiemann surface.
610   $aRoot of unity.
610   $aRotation number.
610   $aSchwarz lemma.
610   $aScientific notation.
610   $aSequence.
610   $aSimply connected space.
610   $aSpecial case.
610   $aSubgroup.
610   $aSubsequence.
610   $aSubset.
610   $aSummation.
610   $aTangent space.
610   $aTheorem.
610   $aTopological space.
610   $aTopology.
610   $aUniform convergence.
610   $aUniformization theorem.
610   $aUnit circle.
610   $aUnit disk.
610   $aUpper half-plane.
610   $aWinding number.
615  0$aFunctions of complex variables.
615  0$aHolomorphic mappings.
615  0$aRiemann surfaces.
676   $a515.93
676   $a515/.93
686   $aSI 830$2rvk
700   $aMilnor$b John W$g(John Willard),$f1931-$040532
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910791879203321
996   $aDynamics in one complex variable$9374228
997   $aUNINA