非线性动力系统和混沌应用导论（第2版）

图书标准信息

• 作者 S.维金斯（S.Wiggins） 著
• 出版社 世界图书出版公司
• 出版时间 2013-05
• 版次 1
• ISBN 9787510058448
• 定价 125.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 844页
• 正文语种 英语

【内容简介】

　　《非线性动力系统和混沌应用导论（第2版）》是一部高年级的本科生和研究生学生学习应用非线性动力学和混沌的入门教程。《非线性动力系统和混沌应用导论（第2版）》的重点讲述大量的技巧和观点，包括了深层次学习本科目的必备的核心知识，这些可以使学生能够学习特殊动力系统并获得学习这些系统大量信息。因此，像工程、物理、化学和生物专业读者不需要另外学习大量的预备知识。新的版本中包括了大量有关不变流形理论和规范模的新材料，拉格朗日、哈密尔顿、梯度和可逆动力系统的也有讨论，也包括了哈密尔顿分叉和环映射的基本性质。本书附了丰富的参考资料和详细的术语表，似的《非线性动力系统和混沌应用导论（第2版）》的可读性更加增大。

【目录】

seriespreface
prefacetothesecondedition
introduction
1equilibriumsolutions，stability，andlinearizedstability
1.1equilibriaofvectorfields
1.2stabilityoftrajectories
1.3maps
1.4someterminologyassociatedwithfixedpoints
1.5applicationtotheunforcedduffingoscillator
1.6exercises

2liapunovfunctions
2.1exercises

3invariantmanifolds：linearandnonlinearsystems
3.1stable，unstable，andcentersubspacesoflinear，autonomousvectorfields
3.2stable，unstable，andcentermanifoldsforfixedpointsofnonlinear，autonomousvectorfields
3.3maps
3.4someexamples
3.5existenceofinvariantmanifolds：themainmethodsofproof，andhowtheywork
3.6time-dependenthyperbolictrajectoriesandtheirstableandunstablemanifolds
3.7invariantmanifoldsinabroadercontext
3.8exercises

4periodicorbits
4.1nonexistenceofperiodicorbitsfortwo-dimensional，autonomousvectorfields
4.2furtherremarksonperiodicorbits
4.3exercises

5vectorfieldspossessinganintegral
5.1vectorfieldsontwo-manifoldshavinganintegral
5.2twodegree-of-freedomhamiltoniansystemsandgeometry
5.3exercises

6indextheory
6.1exercises

7somegeneralpropertiesofvectorfields：existence，uniqueness，differentiability，andflows
7.1existence，uniqueness，differentiabilitywithrespecttoinitialconditions
7.2continuationofsolutions
7.3differentiabilitywithrespecttoparameters
7.4autonomousvectorfields
7.5nonautonomousvectorfields
7.6liouville'stheorem
7.7exercises

8asymptoticbehavior
8.1theasymptoticbehavioroftrajectories
8.2attractingsets，attractors，andbasinsofattraction
8.3thelasalleinvarianceprinciple
8.4attractioninnonautonomoussystems
8.5exercises

9thepoincare-bendixsontheorem
9.1exercises

10poincaremaps
10.1case1：poincar6mapnearaperiodicorbit
10.2case2：thepoincaremapofatime-periodicordinarydifferentialequation
10.3case3：thepoincaremapnearahomoclinicorbit
10.4case4：poincar6mapassociatedwithatwodegree-of-freedomhamiltoniansystem
10.5exercises

11conjugaciesofmaps，andvaryingthecross-section
11.1case1：poincar6mapnearaperiodicorbit：variationofthecross-section
11.2case2：thepoincaremapofatime-periodicordinarydifferentialequation：variationofthecross-section

12structuralstability，genericity，andtransversality
12.1definitionsofstructuralstabilityandgenericity
12.2transversality
12.3exercises

131agrange'sequations
13.1generalizedcoordinates
13.2derivationoflagrange'sequations
13.3theenergyintegral
13.4momentumintegrals
13.5hamilton'sequations
13.6cycliccoordinates，routh'sequations，andreductionofthenumberofequations
13.7variationalmethods
13.8thehamilton-jacobiequation
13.9exercises

14harniltonianvectorfields
14.1symplecticforms
14.2poissonbrackets
14.3symplecticorcanonicaltransformations
14.4transformationofhamilton'sequationsundersymplectictransformations
14.5completelyintegrablehamiltoniansystems
14.6dynamicsofcompletelyintegrablehamiltoniansystemsinaction-anglecoordinates
14.7perturbationsofcompletelyintegrablehamiltoniansystemsinaction-anglecoordinates
14.8stabilityofellipticequilibria
14.9discrete-timehamiltoniandynamicalsystems：iterationofsymplecticmaps
14.10genericpropertiesofhamiltoniandynamicalsystems
14.11exercises

15gradientvectorfields
15.1exercises

16reversibledynamicalsystems
16.1thedefinitionofreversibledynamicalsystems
16.2examplesofreversibledynamicalsystems
16.3linearizationofreversibledynamicalsystems
16.4additionalpropertiesofreversibledynamicalsystems
16.5exercises

17asymptoticallyautonomousvectorfields
17.1exercises

18centermanifolds
18.1centermanifoldsforvectorfields
18.2centermanifoldsdependingonparameters.
18.3theinclusionoflinearlyunstabledirections
18.4centermanifoldsformaps
18.5propertiesofcentermanifolds
18.6finalremarksoncentermanifolds
18.7exercises

19normalforms
19.1normalformsforvectorfields
19.2normalformsforvectorfieldswithparameters
19.3normalformsformaps
19.4exercises
19.5theelphick-tirapegui-brachet-coullet-iooss
19.6exercises
19.7liegroups，liegroupactions，andsymmetries
19.8exercises
19.9normalformcoefficients
19.10hamiltoniannormalforms
19.11exercises
19.12conjugaciesandequivalencesofvectorfields
19.13finalremarksonnormalforms

20bifurcationoffixedpointsofvectorfields
20.1azeroeigenvalue
20.2apureimaginarypairofeigenvalues：thepoincare-andronov-hopfbifurcation
20.3stabilityofbifurcationsunderperturbations
20.4theideaofthecodimensionofabifurcation
20.5versaldeformationsoffamiliesofmatrices
20.6thedouble-zeroeigenvalue：thetakens-bogdanovbifurcation
20.7azeroandapureimaginarypairofeigenvalues：thehopf-steadystatebifurcation
20.8versaldeformationsoflinearhamiltoniansystems
20.9elementaryhamiltonianbifurcations

21bifurcationsoffixedpointsofmaps
21.1aneigenvalueofi
21.2aneigenvalueof-1：perioddoubling
21.3apairofeigenvaluesof1viodulus1：thenaimark-sackerbifurcation
21.4thecodimensionoflocalbifurcationsofmaps
21.5exercises
21.6mapsofthecircle

22ontheinterpretationandapplicationofbifurcationdiagrams：awordofcaution
23thesmalehorseshoe

23.1definitionofthesmalehorseshoemap
23.2constructionoftheinvariantset
23.3symbolicdynamics
23.4thedynamicsontheinvariantset
23.5chaos
23.6finalremarksandobservations

24symbolicdynamics
24.1thestructureofthespaceofsymbolsequences
24.2theshiftmap
24.3exercises

25theconley-moserconditions，or“howtoprovethatadynamicalsystemischaotic”
25.1themaintheorem
25.2sectorbundles
25.3exercises

26dynamicsnearhomoclinicpointsoftwo-dimensionalmaps
26.1heterocliniccycles
26.2exercises

27orbitshomoclinictohyperbolicfixedpointsinthree-dimensionalautonomousvectorfields
27.1thetechniqueofanalysis
27.2orbitshomoclinictoasaddle-pointwithpurelyrealeigenvalues
27.3orbitshomoclinictoasaddle-focus
27.4exercises

28melnikov'smethodforhomoclinicorbitsintwo-dimensional，time-periodicvectorfields
28.1thegeneraltheory
28.2poincaremapsandthegeometryofthemelnikovfunction
28.3somepropertiesofthemelnikovfunction
28.4homoclinicbifurcations
28.5applicationtothedamped，forcedduffingoscillator
28.6exercises

29liapunovexponents
29.1liapunovexponentsofatrajectory
29.2examples
29.3numericalcomputationofliapunovexponents
29.4exercises

30chaosandstrangeattractors
30.1exercises

31hyperbolicinvariantsets：achaoticsaddle
31.1hyperbolicityoftheinvariantcantorsetaconstructedinchapter25
31.2hyperbolicinvariantsetsinr“
31.3aconsequenceofhyperbolicity：theshadowinglemma
31.4exercises
32longperiodsinksindissipativesystemsandellipticislandsinconservativesystems32.1homoclinicbifurcations
32.2newhousesinksindissipativesystems
32.3islandsofstabilityinconservativesystems
32.4exercises

33globalbifurcationsarisingfromlocalcodimension——twobifurcations
33.1thedouble-zeroeigenvalue
33.2azeroandapureimaginarypairofeigenvalues
33.3exercises
34glossaryoffrequentlyusedterms
bibliography
index