Qualitative Theory of Differentiable Dynamical Systems mobi 下载 网盘 caj lrf pdf txt 阿里云

Professor Liao Shantao is an outstanding mathematician in China. As a result of his profound and systematic research work, he won the Mathematics Prize in 1985 which was the first time awarded by the Third World Academy of Sciences for his contributi*** to differentiable dynamical systems and other fields. He also won first-class award of National Natural Science Prize of China in 1987, The Chinese edition of this book collects eight of his major articles on differentiable dynamical systems in the period of 1963 - 1984, arranged in the order according to the dates of submission for publicati***, togethe***ith a preface and an appendix written also by him. Other two appendices A and B, which are original articles by Liao, are added to the translation to the English edition. .

This book introduces systematically the derivation of the two fundamental noti*** of "standard systems of differential equati***" and "obstruction sets" and exhibits their important properties and applicati*** to stability problems.

Preface to the English Edition

Preface to the Chinese Edition.

Chapter 1 Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold

1.1 One-parameter Transformation Groups on Frame Bundles

1.2 Covariant Differentiation, the Function ωk(α)

1.3 The Function logζαk(t)

1.4 The Style Number k*(F)

1.5 On the Determination of the Style Number

1.6 Comparison of Certain Functi***

1.7 3-dimensional Systems with Degenerate Style Numbers

1.8 Square Matrix Rα(t) and Divergence divS

References

Chapter 2 Standard Systems of Differential Equati***

2.1 A Review of Standard Systems of Differential Equati***

2.2 Another Class of Standard Systems of Differential Equati***

2.3 Families Adp of Differential Equati***

2.4 An Application

References

Chapter 3 Obstruction Sets and Strong Transversality Condition

3.1 Introduction

3.2 The Obstruction Set Ob(S)

3.3 Statement of Results

3.4 Trough Sets

References

Chapter 4 Obstruction Sets (I)

4.1 Trough Sets

4.2 Obstruction Set Ob(S)

4.3 Singularities

4.4 Linear Theory of Normal Sets

4.5 Linear Theory of Normal Sets (continued)

References.

Chapter 5 On the Stability Conjecture

5.1 Introduction and Statements of the Main Results

5.2 The Class X*(Mn) of Vector Fields

5.3 Contractible Periodic Orbits

5.4 The Case S ∈ X*(M3)

5.5 The "Sifting" Lemma and the Proof of Theorem 5.4.1

5.6 Proofs of Theorems 5.1.1 and 5.1.2

Appendix

References

Chapter 6 Obstruction Sets (II)

6.1 Introduction

6.2 Obstruction Sets and Minimal Rambling Sets

6.3 Simply Minimal Rambling Sets

*** The Set M(η,T;p) and the Hunched Set R(ζ,p) ∪ L(ζ,p) of S ∈ X*

6.5 Non-Simply Minimal Rambling Sets of S ∈ X* and Proofs of Theorem 6.1.1 and 6.1.2

6.6 On the Sets R(ζ,P) and L(ζ,p)

References

Chapter 7 Standard Systems of Differential Equati*** and Obstruction Sets with Applicati*** to Structural Stability Problems

7.1 Global Linearization of Differential Systems and Expression by Linear Systems

7.2 Standard Systems of Equati***

7.3 A Reduction to Lower Dimension by 1

7.4 Examples of Applicati***

7.5 The Family X* of Differential Systems

7.6 Obstruction Sets

7.7 Simple and Non-Simple Minimal Rambling Sets

7.8 Ω-Stability and Structural Stability

References

Chapter 8 On Characterizati*** of Structural Stability

8.1 Introduction

8.2 Preliminaries. Obstruction Sets and Minimal Rambling Sets

8.3 A Key Step

8.4 Applicati***

References

Appendix to the Chinese Edition

References

Supplement (October 1990)

Appendix A An Extension of the C1 Closing Lemma

A.1 Introduction

A.2 An Abstract of the Proof

A.3 Some Preliminaries

A.4 The Family of Squared Matrices θ(t) (0 ≤ t ＜ ∞o)

A.5 The Proof of Theorem I

A.6 The Proof of Theorem II

A.7 Standard Systems of Differential Equati***

A.8 The Proof of the Main Theorem

A.9 The Case that ωa ∪ αa is Non-empty

References

Appendix B Obstruction Sets, Minimal Rambling Sets and Their Applicati***

B.1 Obstruction Sets

B.2 Relati*** between Obstruction Sets and Transversality Conditi***

B.3 A Filtration for Normal Sets

B.4 Minimal Rambling Sets

B.5 The Families X**(Mn) and X(Mn)

B.6 On Stability of Differential Systems

References

Editor's Postscripts

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