Arnold: Ordinary differential equations Edizioni: MIT Press Anno di pubblicazione: 1998 Euro: 48,00 sconto: 20% pp.: 280 ISBN: 0262510189 Contents: Preface; Frequently Used Notation; Basic Concepts: Phase Spaces and Phase Flows; Vector Fields on the Line; Phase Flows on the Line; Vector Fields and Phase Flows in the Plane; Non autonomous Equations; The Tangent Space; Basic Theorems: The Vector Field near a Nonsingular Point; Applications to the Nonautonomous Case; Applications to Equations of Higher Order; Phase Curves of Autonomous Systems; The Directional Derivative. First Integrals; Conservative Systems with One Degree of Freedom; Linear Systems: Linear Problems; The Exponential of an Operator; Properties of the Exponential; The Determinant of the Exponential; The Case of Distinct Real Eigenvalues; Complexification and Decomplexification; Linear Equations with a Complex Phase Space; Complexification of a Real Linear Equation; Classification of Singular Points of Linear Systems; Topological Classification of Singular Points; Stability of Equilibrium Positions; The Case of Purely Imaginary Eigenvalues; The Case of Multiple Eigenvalues; More on Quasi-Polynomials; Nonautonomous Linear Equations; Linear Equations with Periodic Coefficients; Variation of Constants; Proofs of the Basic Theorems: Contraction Mappings; The Existence, Uniqueness, and Continuity Theorems; The Differentiability Theorem; Differendal Equations on Manifolds: Differentiable Manifolds; The Tangent Bundle. Vector Fields on a Manifold; The Phase Flow Determined by a Vector Field ;The Index of a Singular Point of a Vector Field; Sample Examination Problems; Bibliography