Ordinary differential equations / Vladimir I. Arnold ; translated from the Russian by Roger Cooke.

Translation of: Obyknovennye differentsialʹnye uravneniya. 3rd ed.

Includes bibliographical references and index.

Phase spaces -- Vector fields on the line -- Linear equatins -- Phase flows -- The action of diffeomorphisms on vector fields a and direction fields -- Symmetries -- Rectiftcation theorems -- Applications to equations of higher order than first -- The phase curves of an autonomous system -- The derivative in the direction of a vector field and first integrals -- First-order linear and quasi-linear partial differential equations -- The conservative systems with one degree of freedom -- The exponential fuction -- Propierties of the exponential -- The determinant of an esponential -- Practical computation of the matrix od an exponential - the case when eigenvalues are real and distinet -- Complexification and realification -- The linear equation with a complex phase space -- The complexification of a real linear equation -- The classification of singular points of linear systems -- The topological classification of singular points -- Stability of equilibrium positions -- The case of purely imaginary eigencalues -- The case of multiple eigenvalues -- Quasi polynomials -. Nonautonomous linear equations -- Linear equations with peridic coefficients -- Conttraction mappings -- Proof of the theorems on existence and continuos dependence on the intial conditons -- Differential equations on manifolds.

This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems." L'Enseignment Mathematique "... Arnold's book is unique as a sophisticated but accessible introduction to the modern theory, and we should be grateful that it exists in a convenient language." Mathematical Association of America Monthly