كتاب Multifrequency Oscillations of Nonlinear Systems

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Multifrequency Oscillations of Nonlinear Systems - A. Samoilenko & R. Petryshyn

ويتناول الموضوعات الأتية :

1. AVERAGING METHOD IN OSCILLATION SYSTEMS
WITH VARIABLE FREQUENCIES 9
1. Uniform Estimates for One-Dimensional Oscillation Integrals 9
2. Justification of Averaging Method for Oscillation Systems
with ω = ω(τ ) 21
3. Investigation of Two-Frequency Systems 39
4. Justification of Averaging Method for Oscillation Systems
with ω = ω(x, τ ) 51
5. Averaging over All Fast Variables in Multifrequency Systems
of Higher Approximation 63
2. AVERAGING METHOD IN MULTIPOINT PROBLEMS 71
6. Boundary-Value Problems for Oscillation Systems with
Frequencies Dependent on Time Variable 71
7. Theorem on Justification of Averaging Method on Entire Axis 80
8. Multipoint Problem for Resonance Multifrequency Systems 89
9. Estimates of the Error of Averaging Method for Multipoint
Problems in Critical Case 99
10. Theorems on Existence of Solutions of Boundary-Value
Problems 109
11. Boundary-Value Problems with Parameters 120
vi Contents
3. INTEGRAL MANIFOLDS 133
12. Auxiliary Statements 133
13. Construction of Successive Approximations 145
14. Existence of Integral Manifold 157
15. Conditional Asymptotic Stability of Integral Manifold 165
16. Smoothness of Integral Manifold 174
17. Asymptotic Expansion of Integral Manifold 194
18. Decomposition of Equations in a Neighborhood of
Asymptotically Stable Integral Manifold 206
19. Proof of Theorem 18.1 218
20. Investigation of Second-Order Oscillation Systems 224
21. Weakening of Conditions in the Theorem on Integral Manifold 233
4. INVESTIGATION OF A DYNAMICAL SYSTEM IN
A NEIGHBORHOOD OF A QUASIPERIODIC TRAJECTORY 243
22. Statement and General Description of the Problem 243
23. Theorem on Reducibility 248
24. Variational Equation and Theorem on Attraction to
Quasiperiodic Solutions 261
25. Behavior of Trajectories under Small Perturbations of
a Dynamical System 266
26. The Case of a Toroidal Manifold Filled with Trajectories of
General Form 271
27. Discrete Dynamical System in the Neighborhood of
a Quasiperiodic Trajectory 282
REFERENCES 297

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كتاب Multifrequency Oscillations of Nonlinear Systems 761752

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