Ordinary differential equations / V. I. Arnold ; translated and edited by Richard A. Silverman.
Idioma: Inglés Lenguaje original: Ruso Editor: Cambridge, Mass. : MIT Press, c1973Descripción: viii, 280 p. : il. ; 24 cmISBN: 0262010372Títulos uniformes: Obyknovennye differentsial´nye uravneniia. Inglés Otra clasificación: 34-01 (34Cxx 37-01)Preface vii Frequently Used Notation ix 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 Equations on 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]
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Traducción de: Obyknovennye differentsial´nye uravneniia, 1971.
Bibliografía: p. [273].
Preface vii --
Frequently Used Notation ix --
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 Equations on 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] --
MR, 50 #13677 (para la ed. original en ruso)
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