Dynamical Systems英文学习资料

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1、DynamicalSystemsShlomoSternbergJune4,20092Contents1Iterationandxedpoints.91.1Squareroots..............................91.1.1Analyzingthesteps.....................91.2Newton'smethod...........................111.2.1Axedpointoftheiterationschemeisasolutiontoourprob

2、lem............................121.2.2Thegutsofthemethod....................121.2.3Avectorversion........................131.2.4ProblemswiththeimplementationofNewton'smethod.141.2.5Theexistencetheorem....................151.2.6Review.............................181

3、.2.7Basinsofattraction......................181.2.8Cayley'scomplexversion..................201.3TheimplicitfunctiontheoremviaNewton'smethod........221.3.1Thecontinuity,dierentiabilityoftheimplicitfunction,andthecomputationofitsderivative............231.4Attractors

4、andrepellers........................251.4.1Attractors...........................251.4.2Thebasinofattractionofanattractor...........251.4.3Repellers............................261.4.4Superattractors........................261.4.5Notationforiteration.................

5、....261.4.6Periodicpoints.........................261.5Renormalizationgroup........................271.6Iterationforkindergarten.......................312Bifurcations.332.1Thelogisticfamily...........................332.1.10<1:...........................342.1.2=

6、1..............................342.1.3>1..............................342.1.41<<2............................352.1.5=2-thexedpointissuperattractive..........372.1.62<<3............................3734CONTENTS2.1.7=3:.............................402.1.8>3,poi

7、ntsofperiodtwoappear..............40p2.1.93<<1+6........................412.1.10Superattractingperiodtwopoints..............43p2.1.111+6<...........................432.1.12Reprise.............................432.2Thefoldbifurcation..........................462.3T

8、heperioddoublingbifurcation...................512.3.1Descriptionoftheperioddoublingbifurcation......512.3.2Statementoftheperioddoublingbifurcatio