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平面动力系统的若干经典问题(英文版)
  • 书号:9787030408433
    作者:刘一戎,李继彬,黄文韬文
  • 外文书名:
  • 丛书名:数学专著丛书
  • 装帧:圆脊精装
    开本:16
  • 页数:388
    字数:450
    语种:
  • 出版社:科学出版社
    出版时间:2015-11-18
  • 所属分类:O 数理科学和化学 O69 应用化学
  • 定价: ¥138.00元
    售价: ¥110.40元
  • 图书介质:
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浅水波,非线性光学、电磁学、等离子物理、凝聚态物理、生物及化学、通讯等领域均存在非线性波运动.对其数学模型--波方程的解研究有重要价值.上世纪90年代,数学家发现了行波方程的非光滑的孤粒子解(peakon)、有限支集解(compacton)和圈解(loopsolution)等,为理解这些解,特别是非光滑解的出现,导致用动力系统的分支理论及方法对奇行波方程进行研究的新方向.本书介绍两类奇行波方程的研究的动力系统方法,及对大量数学物理问题的应用。
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目录


  • 2.4 The Algebraic Construction of Singular Values 83



    2.5 Elementary Generalized Rotation Invariants of the Cubic Systems 88

    2.6 Singular Point Values and Integrability Condition of the QuadraticSystems 90

    2.7 Singular Point Values and Integrability Condition of the Cubic Systems Having Homogeneous Nonlinearities . . . . . . 93 3 Multiple Hopf Bifurcations 97

    3.1 The Zeros of Successor Functions in the Polar Coordinates . . . . . 97

    3.2 AnalyticEquivalence 100

    QuasiSuccessor Function 102



    3.3



    3.4 Bifurcations of Limit Circle of a Class of Quadratic Systems . 108 4 Isochronous Center In Complex Domain .111

    4.1 Isochronous Centers and Period Constants 111



    xii Contents

    4.2 Linear Recursive Formulas to Compute Period Constants 116

    4.3 Isochronous Center for a Class of Quintic System in the Complex Domain 122 123

    4.3.1 The Conditions of Isochronous Center Under Condition C1

    124





    4.3.2 The Conditions of Isochronous Center Under Condition C2

    127





    4.3.3 The Conditions of Isochronous Center Under Condition C3

    . . . 128



    4.3.4 Non-Isochronous Center under Condition C4 and C4 .

    4.4 TheMethodofTime-AngleDi.erence 128



    4.5 The Conditions of Isochronous Center of the Origin for a Cubic System 134

    5 Theory of Center-Focus and Bifurcation of Limit Cycles at In.nity of a Class of Systems 138

    5.1 De.nition of the Focal Values of In.nity 138

    Conversionof Questions 141



    5.2

    5.3 Method of Formal Series and Singular Point Value of In.nity . 144

    5.4 The Algebraic Construction of Singular Point Values of In.nity . 156

    5.5 Singular Point Values at In.nity and Integrable Conditions for a Class of Cubic System 161

    5.6 Bifurcation of Limit Cycles at In.nity 168



    5.7 Isochronous Centers at In.nity of a Polynomial Systems 172

    5.7.1 Conditions of Complex Center for System (5.7.6) 173







    5.7.2 Conditions of Complex Isochronous Center for System (5.7.6) . . 176

    6 Theory of Center-Focus and Bifurcations of Limit Cycles for aClass of MultipleSingularPoints . 180

    6.1 Succession Function and Focal Values for a Class of Multiple Singular Points 180 Conversion of the Questions 182

    6.2

    6.3 Formal Series, Integral Factors and Singular Point Values for a Class of Multiple Singular Points 184

    6.4 The Algebraic Structure of Singular Point Values of a Class of Multiple Singular Points 196

    6.5 Bifurcation of Limit Cycles From a Class of Multiple Singular Points 198

    6.6 Bifurcation of Limit Cycles Created from a Multiple Singular Point for a Class of Quartic System 199

    6.7 Quasi Isochronous Center of Multiple Singular Point for

    Contents xiii

    a Class of Analytic System 202

    7 OnQuasi Analytic Systems 205



    7.1 Preliminary 205

    Reduction of the Problems 208



    7.2

    7.3 Focal Values, Periodic Constants and First Integrals of (7.2.3) 210



    7.4 Singular Point Values and Bifurcations of Limit Cycles of Quasi-Quadratic Systems 214

    7.5 Integrability of Quasi-Quadratic Systems 217



    7.6 Isochronous Center of Quasi-Quadratic Systems 219





    7.6.1 The Problem of Complex Isochronous Centers Under

    219



    the Condition of C1



    7.6.2 The Problem of Complex Isochronous Centers Under

    222



    the Condition of C2

    7.6.3 The Problem of Complex Isochronous Centers Under the Other Conditions 225

    7.7 Singular Point Values and Center Conditions for a Class of Quasi-Cubic Systems 228

    8 Local and Non-Local Bifurcations of Perturbed Zq-Equivariant Hamiltonian Vector Fields 232

    8.1 Zq-Equivariant Planar Vector Fields and an Example 232



    8.2 The Method of Detection Functions: Rough Perturbations of Zq-Equivariant Hamiltonian Vector Fields 242

    8.3 Bifurcations of Limit Cycles of a Z2-Equivariant Perturbed Hamiltonian Vector Fields 244

    8.3.1 Hopf Bifurcation Parameter Values 246



    8.3.2 Bifurcations From Heteroclinic or Homoclinic Loops 247



    8.3.3 The Values of Bifurcation Directions of Heteroclinic and Homoclinic Loops 252

    8.3.4 Analysis and Conclusions 255



    8.4 The Rate of Growth of Hilbert Number H(n)with n 258



    8.4.1 Preliminary Lemmas 259



    8.4.2 A Correction to the Lower Bounds of H(2k .1) Given in [Christopher and Lloyd, 1995] 262

    8.4.3 A New Lower Bound for H(2k .1) 265



    8.4.4 Lower Bound for H(3 ]]>
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