000			03614nam a2200325 i 4500
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008			030214t20001991enka b 001 0 eng d
020			_a0387951512
040			_aNXW _cNXW _dOCLCQ _dDAY
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA297.8 _b.B43 2000
100	1		_aBeardon, Alan F _986446 _eaut
245	1	0	_aIteration of rational functions : _bcomplex analytic dynamical systems / _cAlan F. Beardon
264		1	_aNew York : _bSpringer, _c[2000]
264		4	_c©1991
300			_axvi, 280 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aGraduate texts in mathematics ; _v132
504			_aIncludes bibliographical references (pages [273]-277) and indexes
505	0	0	_tTable Of Contents: _tPreface _tPrerequisites _tExamples _tIntroduction _tIteration of Mobius Transformations _tIteration of z ↦ z2 _tTchebychev Polynomials _tIteration of z andmap z2-1 _tIteration of z andmap z2 + c _tIteration of z andmap z + 1/z _tIteration of z andmap 2z - 1/z _tNewton's Approximation _tGeneral Remarks _tRational Maps _tThe Extended Complex Plane _tRational Maps _tThe Lipschitz Condition _tConjugacy _tValency _tFixed Points _tCritical Points _tA Topology on the Rational Functions _tThe Fator and Julia Sets _tThe Fatou and Julia Sets _tCompletely Invariant Sets _tNormal Families and Equicontinuity _tThe Hyperbolic Metric _tProperties of the Julia Set _tExceptional Points _tProperties of the Julia Set _tRational Maps with Empty Fatou Set _tElliptic Functions _tThe Structure of the Fatou Set _tThe Toplogy of the Sphere _tCompletely Invariant Components of the Fatou Set _tThe Euler Characteristic _tThe Riemann-Hurwitz Formula for Covering Maps _tMaps Between Components of the Fatou Set _tThe Number of Components of the Fatou Set _tComponents of the Julia Set _tPeriodic Points _tThe Classification of Periodic Points _tThe Ecistence of Periodic Points _t(Super) Atracting Cycles _tRepelling Cycles _tRationally Indifferent Cycles _tIrrationally Indifferent Cycles in F _tIrrationally Indifferent Cycles in J _tThe Proof of the Existence of Periodic Points _tThe Julia Set and Periodic Points _tLocal Conjugacy _tInfinite Products _tThe Universal Covering Surface _tForward Invariant Components _tThe Five Possibilities _tLimit Functions _tParabolic Domains _tSiegel Discs and Herman Rings _tConnectivity of Invariant Components _tThe No Wandering Domains Theorem _tThe No Wandering Domains Theorem _tA Preliminary Result _tConformal Structures _tQuasiconformal Conjugates of Rational Maps _tBoundary Values of Conjugate Maps _tThe Proof of Theorem 8.1.2 _tCritical Points _tIntroductory Remarks _tThe Normality of Inverse Maps _tCritical Points and Periodic Domains _tApplications _tThe Fatou Set of a Polynomial _tThe Number of Non-Repelling Cycles _tExpanding Maps _tJulia Sets as Cantor Sets _tJulia Sets as Jordan Curves _tThe Mandelbrot Set _tHausdorff Dimension _tHausdorff Dimension _tComputing Dimensions _tThe Dimension of Julia Sets _tExamples _tSmooth Julia Sets _tDendrites _tComponents of F of Infinite Connectivity _tF with Infinitely Connected and Simply Connected Components _tJ with Infinitely Many Non-Degenerate Components _tF of Infinite Connectivity with Critical Points in J _tA Finitely Connected Component of F _tJ Is a Cantor Set of Circles _tThe Function (z - 2)2/z2 _tReferences _tIndex of Examples _tIndex
650		0	_aIterative methods (Mathematics)
650		0	_aMappings (Mathematics)
830		0	_919347 _aGraduate texts in mathematics ; _v132
900			_bsatın
942			_2lcc _cKT
999			_c14331 _d14331