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Multifrequency Oscillations of Nonlinear Systems
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- Multifrequency Oscillations of Nonlinear Systems By A. Samoilenko
- Contents
- INTRODUCTION
- 1. AVERAGING METHOD IN OSCILLATION SYSTEMS WITH VARIABLE FREQUENCIES
- 2. Justification of Averaging Method for Oscillation Systems with ω = ω (τ )
- 3. Investigation of Two-Frequency Systems
- 4. Justification of Averaging Method for Oscillation Systems with ω = ω (x, τ )
- 5. Averaging over All Fast Variables in Multifrequency Systems of Higher Approximation
- 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
- 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 a 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
- 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