Multifrequency oscillations of nonlinear systems
Author(s)
Bibliographic Information
Multifrequency oscillations of nonlinear systems
（Mathematics and its applications, v. 567）
Kluwer Academic, c2004
Available at 15 libraries
Note
Includes bibliographical references
Description and Table of Contents
Description
In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.
In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.
This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.
Table of Contents
Introduction.
1: Averaging Method in Oscillation Systems with Variable Frequencies. 1. Uniform Estimates for One-Dimensional Oscillation Integrals. 2. Justification of Averaging Method for Oscillation Systems with omega = omega(tau). 3. Investigation of Two-Frequency Systems. 4. Justification of Averaging Method for Oscillation Systems with omega = omega(x, tau). 5. Averaging over All Fast Variables in Multifrequency Systems of Higher Approximation.
2: Averaging Method in Multipoint Problems. 6. Boundary-Value Problems for Oscillation Systems with Frequencies Dependent on Time Variable. 7. Theorem on Justification of Averaging Method on Entire Axis. 8. Multipoint Problem for Resonance Multifrequency Systems. 9. Estimates of the Error of Averaging Method for Multipoint Problems in Critical Case. 10. Theorems on Existence of Solutions of Boundary-Value Problems. 11. Boundary-Value Problems with Parameters.
3: Integral Manifolds. 12. Auxiliary Statements. 13. Construction of Successive Approximations. 14. Existence of Integral Manifold. 15. Conditional Asymptotic Stability of Integral Manifold. 16. Smoothness of Integral Manifold. 17. Asymptotic Expansion of Integral Manifold. 18. Decomposition of Equations in the Neighborhood of Asymptotically Stable Integral Manifold. 19. Proof of Theorem 18.1. 20. Investigation of Second-Order Oscillation Systems. 21. Weakening of Conditions in the Theorem on Integral Manifold.
4: Investigation of a Dynamical System in the Neighborhood of Quasiperiodic Trajectory. 22. Statement and General description of the Problem. 23. Theorem on Reducibility. 24. Variational Equation and Theorem on Attraction to Quasiperiodic Solutions. 25. Behavior of Trajectories under Small Perturbations of a Dynamical System. 26. The Case of a Toroidal Manifold Filled with Trajectories of General Form. 27. Discrete Dynamical System in the Neighborhood of a Quasiperiodic Trajectory.
References.
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