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1.

図書
図書
1. Geometrical methods in the theory of ordinary differential equations. 2nd ed (: us ; : gw)
V.I. Arnold ; translated by Joseph Szücs ; English translation edited by Mark Levi
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xii, 351 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 250
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目次情報: 続きを見る
Special Equations
First-Order Partial Differential Equations
Structural Stability
Perturbation Theory
Normal Forms
Local Bifurcation Theory
Samples of Examination Problems
Index
Special Equations
First-Order Partial Differential Equations
Structural Stability
2.

図書
図書
2. Ordinary differential equations (: gw ; : us)
Vladimir I. Arnol'd ; translated from the Russian by Roger Cooke
出版情報: Berlin : Tokyo : Springer-Verlag, c1992  334 p. ; 24 cm
シリーズ名: Springer textbook
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目次情報: 続きを見る
Preface
Frequently Used Notation
Basic Concepts / 1：
Phase Spaces and Phase Flows
Vector Fields on the Line / 2：
Phase Flows on the Line / 3：
Vector Fields and Phase Flows in the Plane / 4：
Nonautonomous Equations / 5：
The Tangent Space / 6：
Basic Theorems
The Vector Field near a Nonsingular Point / 7：
Applications to the Nonautonomous Case / 8：
Applications to Equations of Higher Order / 9：
Phase Curves of Autonomous Systems / 10：
The Directional Derivative. First Integrals / 11：
Conservative Systems with One Degree of Freedom / 12：
Linear Systems
Linear Problems / 13：
The Exponential of an Operator / 14：
Properties of the Exponential / 15：
The Determinant of the Exponential / 16：
The Case of Distinct Real Eigenvalues / 17：
Complexification and Decomplexification / 18：
Linear Equations with a Complex Phase Space / 19：
Complexification of a Real Linear Equation / 20：
Classification of Singular Points of Linear Systems / 21：
Topological Classification of Singular Points / 22：
Stability of Equilibrium Positions / 23：
The Case of Purely Imaginary Eigenvalues / 24：
The Case of Multiple Eigenvalues / 25：
More on Quasi-Polynomials / 26：
Nonautonomous Linear Equations / 27：
Linear Equations with Periodic Coefficients / 28：
Variation of Constants / 29：
Proofs of the Basic Theorems
Contraction Mappings / 30：
The Existence, Uniqueness, and Continuity Theorems / 31：
The Differentiable Manifolds / 33：
The Tangent Bundle. Vector Fields on a Manifold / 34：
The Phase Flow Determined by a Vector Field / 35：
The Index of a Singular Point of a Vector Field / 36：
Sample Examination Problems
Bibliography
Index
Preface
Frequently Used Notation
Basic Concepts / 1：
3.

図書
図書
3. Ordinary differential equations (: hard ; : pbk)
V.I. Arnold ; translated and edited by Richard A. Silverman
出版情報: Cambridge : MIT Press, c1973  viii, 280 p. ; 23 cm
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目次情報: 続きを見る
Preface
Frequently Used Notation
Basic Concepts / 1：
Phase Spaces and Phase Flows
Vector Fields on the Line / 2：
Phase Flows on the Line / 3：
Vector Fields and Phase Flows in the Plane / 4：
Nonautonomous Equations / 5：
The Tangent Space / 6：
Basic Theorems
The Vector Field near a Nonsingular Point / 7：
Applications to the Nonautonomous Case / 8：
Applications to Equations of Higher Order / 9：
Phase Curves of Autonomous Systems / 10：
The Directional Derivative. First Integrals / 11：
Conservative Systems with One Degree of Freedom / 12：
Linear Systems
Linear Problems / 13：
The Exponential of an Operator / 14：
Properties of the Exponential / 15：
The Determinant of the Exponential / 16：
The Case of Distinct Real Eigenvalues / 17：
Complexification and Decomplexification / 18：
Linear Equations with a Complex Phase Space / 19：
Complexification of a Real Linear Equation / 20：
Classification of Singular Points of Linear Systems / 21：
Topological Classification of Singular Points / 22：
Stability of Equilibrium Positions / 23：
The Case of Purely Imaginary Eigenvalues / 24：
The Case of Multiple Eigenvalues / 25：
More on Quasi-Polynomials / 26：
Nonautonomous Linear Equations / 27：
Linear Equations with Periodic Coefficients / 28：
Variation of Constants / 29：
Proofs of the Basic Theorems
Contraction Mappings / 30：
The Existence, Uniqueness, and Continuity Theorems / 31：
The Differentiable Manifolds / 33：
The Tangent Bundle. Vector Fields on a Manifold / 34：
The Phase Flow Determined by a Vector Field / 35：
The Index of a Singular Point of a Vector Field / 36：
Sample Examination Problems
Bibliography
Index
Preface
Frequently Used Notation
Basic Concepts / 1：
4.

図書
図書
4. Ordinary differential equations and smooth dynamical systems (: gw ; : us)
D.V. Anosov, V.I. Arnold (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  vi, 233 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 1 . Dynamical systems ; 1
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5.

図書
図書
5. Thirteen papers on functional analysis and differential equations
V.I. Arnolʹd ...[et al.]
出版情報: Providence, R.I. : American Mathematical Society, 1969  iv, 269 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 79
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