Local methods in nonlinear differential equations
著者
書誌事項
Local methods in nonlinear differential equations
（Springer series in Soviet mathematics）
Springer-Verlag, c1989
- : Berlin
- : New York
- タイトル別名
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Lokalʹnyĭ metod nelineĭnogo analiza different︠s︡ialʹnykh uravneniĭ
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注記
Translation of: Lokalʹnyĭ metod nelineĭnogo analiza different︠s︡ialʹnykh uravneniĭ
Includes index
収録内容
- Pt. 1. The local method of nonlinear analysis of differential equations
- Pt. 2. The sets of analyticity of a normalizing transformation
内容説明・目次
内容説明
The method of normal forms is usually attributed to Poincare although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students."
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