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024 7 $a10.1515/9781400882557
035   $a(CKB)3710000000631328
035   $a(MiAaPQ)EBC4738743
035   $a(DE-B1597)467921
035   $a(OCoLC)954123972
035   $a(OCoLC)990384277
035   $a(DE-B1597)9781400882557
035   $a(EXLCZ)993710000000631328
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aComplex Dynamics and Renormalization (AM-135), Volume 135 /$fCurtis T. McMullen
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1995
215   $a1 online resource (229 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v317
311   $a0-691-02982-2 
311   $a0-691-02981-4 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tChapter 1. Introduction -- $tChapter 2. Background in conformal geometry -- $tChapter 3. Dynamics of rational maps -- $tChapter 4. Holomorphic motions and the Mandelbrot set -- $tChapter 5. Compactness in holomorphic dynamics -- $tChapter 6. Polynomials and external rays -- $tChapter 7. Renormalization -- $tChapter 8. Puzzles and infinite renormalization -- $tChapter 9. Robustness -- $tChapter 10. Limits of renormalization -- $tChapter 11. Real quadratic polynomials -- $tAppendix A. Orbifolds -- $tAppendix B. A closing lemma for rational maps -- $tBibliography -- $tIndex
330   $aAddressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.
410  0$aAnnals of mathematics studies ;$vno. 135.
606   $aRenormalization (Physics)
606   $aPolynomials
606   $aDynamics
606   $aMathematical physics
610   $aAnalytic function.
610   $aAttractor.
610   $aAutomorphism.
610   $aBernhard Riemann.
610   $aBounded set.
610   $aBranched covering.
610   $aCantor set.
610   $aCardioid.
610   $aChain rule.
610   $aCoefficient.
610   $aCombinatorics.
610   $aComplex manifold.
610   $aComplex plane.
610   $aComplex torus.
610   $aConformal geometry.
610   $aConformal map.
610   $aConjecture.
610   $aConnected space.
610   $aCovering space.
610   $aCyclic group.
610   $aDegeneracy (mathematics).
610   $aDense set.
610   $aDiagram (category theory).
610   $aDiameter.
610   $aDifferential geometry of surfaces.
610   $aDihedral group.
610   $aDimension (vector space).
610   $aDimension.
610   $aDisjoint sets.
610   $aDisk (mathematics).
610   $aDynamical system.
610   $aEndomorphism.
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aErgodic theory.
610   $aEuler characteristic.
610   $aFilled Julia set.
610   $aGeometric function theory.
610   $aGeometry.
610   $aHausdorff dimension.
610   $aHolomorphic function.
610   $aHomeomorphism.
610   $aHomology (mathematics).
610   $aHyperbolic geometry.
610   $aImplicit function theorem.
610   $aInjective function.
610   $aInteger matrix.
610   $aInterval (mathematics).
610   $aInverse limit.
610   $aJulia set.
610   $aKleinian group.
610   $aLimit point.
610   $aLimit set.
610   $aLinear map.
610   $aMandelbrot set.
610   $aManifold.
610   $aMarkov partition.
610   $aMathematical induction.
610   $aMaxima and minima.
610   $aMeasure (mathematics).
610   $aModuli (physics).
610   $aMonic polynomial.
610   $aMontel's theorem.
610   $aMöbius transformation.
610   $aNatural number.
610   $aOpen set.
610   $aOrbifold.
610   $aPeriodic point.
610   $aPermutation.
610   $aPoint at infinity.
610   $aPole (complex analysis).
610   $aPolynomial.
610   $aProper map.
610   $aQuadratic differential.
610   $aQuadratic function.
610   $aQuadratic.
610   $aQuasi-isometry.
610   $aQuasiconformal mapping.
610   $aQuotient space (topology).
610   $aRemovable singularity.
610   $aRenormalization.
610   $aRiemann mapping theorem.
610   $aRiemann sphere.
610   $aRiemann surface.
610   $aRigidity theory (physics).
610   $aScalar (physics).
610   $aSchwarz lemma.
610   $aScientific notation.
610   $aSpecial case.
610   $aStructural stability.
610   $aSubgroup.
610   $aSubsequence.
610   $aSymbolic dynamics.
610   $aTangent space.
610   $aTheorem.
610   $aUniformization theorem.
610   $aUniformization.
610   $aUnion (set theory).
610   $aUnit disk.
610   $aUpper and lower bounds.
615  0$aRenormalization (Physics)
615  0$aPolynomials.
615  0$aDynamics.
615  0$aMathematical physics.
676   $a530.1/43/0151
700   $aMcMullen$b Curtis T., $061159
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154745403321
996   $aComplex Dynamics and Renormalization (AM-135), Volume 135$92785741
997   $aUNINA