Asymptotic solutions of strongly nonlinear systems of differential equations

✍ Scribed by Valery V. Kozlov, Stanislav D. Furta (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 278
• Series: Springer monographs in mathematics
• Edition: 1
• Category: Library

✦ Synopsis

The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone.

The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.

✦ Table of Contents

Front Matter....Pages i-xix
Semi-quasihomogeneous Systems of Differential Equations....Pages 1-75
The Critical Case of Pure Imaginary Roots....Pages 77-130
Singular Problems....Pages 131-167
Inversion Problem for the Lagrange Theorem on the Stability of Equilibrium and Related Problems....Pages 169-214
Back Matter....Pages 215-262

✦ Subjects

Ordinary Differential Equations;Dynamical Systems and Ergodic Theory;Mathematical Methods in Physics