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010   $a0-691-00257-6
010   $a1-4008-6518-2
024 7 $a10.1515/9781400865185
035   $a(CKB)3710000000221858
035   $a(EBL)1756204
035   $a(OCoLC)887499708
035   $a(SSID)ssj0001333670
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035   $a(PQKBTitleCode)TC0001333670
035   $a(PQKBWorkID)11394032
035   $a(PQKB)11541986
035   $a(MiAaPQ)EBC1756204
035   $a(DE-B1597)447948
035   $a(OCoLC)922696192
035   $a(DE-B1597)9781400865185
035   $a(Au-PeEL)EBL1756204
035   $a(CaPaEBR)ebr10907682
035   $a(CaONFJC)MIL636773
035   $a(EXLCZ)993710000000221858
100   $a20140822h19981998  uy             0
101 0 $aeng
135   $aur|nu---|u||u
181   $ctxt
182   $cc
183   $acr
200 14$aThe real Fatou conjecture /$fby Jacek Graczyk and Grzegorz Swiatek
210  1$aPrinceton, New Jersey :$cPrinceton University Press,$d1998.
210  4$d{copy}1998
215   $a1 online resource (158 p.)
225 1 $aAnnals of Mathematics Studies ;$vNumber 144
300   $aDescription based upon print version of record.
311 0 $a1-322-05522-X 
311 0 $a0-691-00258-4 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tChapter 1. Review of Concepts --$tChapter 2. Quasiconformal Gluing --$tChapter 3. Polynomial-Like Property --$tChapter 4. Linear Growth of Moduli --$tChapter 5. Quasi conformal Techniques --$tBibliography --$tIndex
330   $aIn 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.
410  0$aAnnals of mathematics studies ;$vNumber 144.
606   $aGeodesics (Mathematics)
606   $aPolynomials
606   $aMappings (Mathematics)
610   $aAbsolute value.
610   $aAffine transformation.
610   $aAlgebraic function.
610   $aAnalytic continuation.
610   $aAnalytic function.
610   $aArithmetic.
610   $aAutomorphism.
610   $aBig O notation.
610   $aBounded set (topological vector space).
610   $aC0.
610   $aCalculation.
610   $aCanonical map.
610   $aChange of variables.
610   $aChebyshev polynomials.
610   $aCombinatorics.
610   $aCommutative property.
610   $aComplex number.
610   $aComplex plane.
610   $aComplex quadratic polynomial.
610   $aConformal map.
610   $aConjecture.
610   $aConjugacy class.
610   $aConjugate points.
610   $aConnected component (graph theory).
610   $aConnected space.
610   $aContinuous function.
610   $aCorollary.
610   $aCovering space.
610   $aCritical point (mathematics).
610   $aDense set.
610   $aDerivative.
610   $aDiffeomorphism.
610   $aDimension.
610   $aDisjoint sets.
610   $aDisjoint union.
610   $aDisk (mathematics).
610   $aEquicontinuity.
610   $aEstimation.
610   $aExistential quantification.
610   $aFibonacci.
610   $aFunctional equation.
610   $aFundamental domain.
610   $aGeneralization.
610   $aGreat-circle distance.
610   $aHausdorff distance.
610   $aHolomorphic function.
610   $aHomeomorphism.
610   $aHomotopy.
610   $aHyperbolic function.
610   $aImaginary number.
610   $aImplicit function theorem.
610   $aInjective function.
610   $aInteger.
610   $aIntermediate value theorem.
610   $aInterval (mathematics).
610   $aInverse function.
610   $aIrreducible polynomial.
610   $aIteration.
610   $aJordan curve theorem.
610   $aJulia set.
610   $aLimit of a sequence.
610   $aLinear map.
610   $aLocal diffeomorphism.
610   $aMathematical induction.
610   $aMathematical proof.
610   $aMaxima and minima.
610   $aMeromorphic function.
610   $aModuli (physics).
610   $aMonomial.
610   $aMonotonic function.
610   $aNatural number.
610   $aNeighbourhood (mathematics).
610   $aOpen set.
610   $aParameter.
610   $aPeriodic function.
610   $aPeriodic point.
610   $aPhase space.
610   $aPoint at infinity.
610   $aPolynomial.
610   $aProjection (mathematics).
610   $aQuadratic function.
610   $aQuadratic.
610   $aQuasiconformal mapping.
610   $aRenormalization.
610   $aRiemann sphere.
610   $aRiemann surface.
610   $aSchwarzian derivative.
610   $aScientific notation.
610   $aSubsequence.
610   $aTheorem.
610   $aTheory.
610   $aTopological conjugacy.
610   $aTopological entropy.
610   $aTopology.
610   $aUnion (set theory).
610   $aUnit circle.
610   $aUnit disk.
610   $aUpper and lower bounds.
610   $aUpper half-plane.
610   $aZ0.
615  0$aGeodesics (Mathematics)
615  0$aPolynomials.
615  0$aMappings (Mathematics)
676   $a516.3/62
700   $aGraczyk$b Jacek$066776
702   $aSwiatek$b Grzegorz$f1964-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910816804503321
996   $aReal Fatou conjecture$91501746
997   $aUNINA