- 作 者：V.I.ARNOLD
- 出 版 社：THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY
- 出版年份：1973
- ISBN：0262010372
- 标注页数：280 页
- PDF页数：289 页
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1 Basic Concepts 1
1 Phase Spaces and Phase Flows 1
2 Vector Fields on the Line 11
3 Phase Flows on the Line 19
4 Vector Fields and Phase Flows in the Plane 24
5 Nonautonomous Equations 28
6 The Tangent Space 33
2 Basic Theorems 48
7 The Vector Field near a Nonsingular Point 48
8 Applications to the Nonautonomous Case 56
9 Applications to Equations of Higher Order 59
10 Phase Curves of Autonomous Systems 68
11 The Directional Derivative.First Integrals 72
12 Conservative Systems with One Degree of Freedom 79
3 Linear Systems 95
13 Linear Problems 95
14 The Exponential of an Operator 97
15 Properties of the Exponential 104
16 The Determinant of the Exponential 111
17 The Case of Distinct Real Eigenvalues 115
18 Complexification and Decomplexification 119
19 Linear Equations with a Complex Phase Space 124
20 Complexification of a Real Linear Equation 129
21 Classification of Singular Points of Linear Systems 139
22 Topological Classification of Singular Points 143
23 Stability of Equilibrium Positions 154
24 The Case of Purely Imaginary Eigenvalues 160
25 The Case of Multiple Eigenvalues 167
26 More on Quasi-Polynomials 176
27 Nonautonomous Linear Equations 188
28 Linear Equations with Periodic Coefficients 199
29 Variation of Constants 208
4 Proofs of the Basic Theorems 211
30 Contraction Mappings 211
31 The Existence, Uniqueness, and Continuity Theorems 213
32 The Differentiability Theorem 223
5 Differential Equationson Manifolds 233
33 Differentiable Manifolds 233
34 The Tangent Bundle.Vector Fields on a Manifold 243
35 The Phase Flow Determined by a Vector Field 250
36 The Index of a Singular Point of a Vector Field 254
Sample Examination Problems 269
Bibliography 273
Index 275