Local Methods in Nonlinear Differential Equations : Part I the Local Method of Nonlinear Analysis of Differential Equations Part II the Sets of Analyticity of a Normalizing Transformation

Bruno, Alexander D.; Hovingh, William (TRN); Coleman, Courtney S. (TRN)

ISBN 10: 364264788X / ISBN 13: 9783642647888

Published by Springer, 2011

About this Item

Seller Inventory # 18723171-n

Bibliographic Details

• Title: Local Methods in Nonlinear Differential Equations : Part I the Local Method of Nonlinear Analysis of Differential Equations Part II the Sets of Analyticity of a Normalizing Transformation
• Publisher: Springer
• Publication Date: 2011
• Language: English
• ISBN 10: 364264788X
• ISBN 13: 9783642647888
• Binding: Soft cover
• Condition: New

About this title

Synopsis

The method of normal forms is usually attributed to Poincaré 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.