β Scribed by Yu. A. Mitropolsky, A. K. Lopatin (auth.)
No coin nor oath required. For personal study only.
This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the PoincarΓ©--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems.
This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
Front Matter....Pages i-ix
Introduction....Pages 1-12
Vector Fields, Algebras and Groups Generated by a System of Ordinary Differential Equations and their Properties....Pages 13-50
Decomposition of Systems of Ordinary Differential Equations....Pages 51-114
Asymptotic decomposition of systems of ordinary differential equations with a small parameter....Pages 115-158
Asymptotic Decomposition of Almost Linear Systems of Differential Equations with Constant Coefficients and Perturbations in the Form of Polynomials....Pages 159-218
Asymptotic Decomposition of Differential Systems with Small Parameter in the Representation Space of Finite-dimensional Lie Group....Pages 219-258
Asymptotic Decomposition of Differential Systems where Zero Approximation has Special Properties....Pages 259-304
Asymptotic Decomposition of Pfaffian Systems with a Small Parameter....Pages 305-338
Back Matter....Pages 339-382
Ordinary Differential Equations; Partial Differential Equations; Topological Groups, Lie Groups; Applications of Mathematics; Vibration, Dynamical Systems, Control
π SIMILAR VOLUMES
Title Page; Copyright; Contents; Introduction; Bibliographical Comments; References; Index.
<p>The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if n
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of w
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustra