Free Delivery Over $100
|
|
|||
|
||||
OverviewThe 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. Full Product DetailsAuthor: Alexander D. Bruno , William Hovingh , Courtney S. ColemanPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1989 Dimensions: Width: 15.50cm , Height: 1.90cm , Length: 23.50cm Weight: 0.552kg ISBN: 9783642647888ISBN 10: 364264788 Pages: 348 Publication Date: 16 September 2011 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI The Local Method of Nonlinear Analysis of Differential Equations.- I. Foundations of the Local Method.- II. A System of Two Differential Equations.- III. The Normal Form of a System on n Differential Equations.- IV. On the Newton Polyhedron.- V. Applications of the Normal Form in Mechanics.- II The Sets of Analyticity of a Normalizing Transformation.- Author’ Comments (1986).- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
