Methods of Accelerated Convergence in Nonlinear Mechanics - Brossura

Bogoljubov, N.N. N.; Mitropoliskii, J.A.; Samoilenko, A.M.

Brossura

ISBN 10: 3642619029 ISBN 13: 9783642619021

Casa editrice: Springer, 2011

Riassunto

This monograph deals with some of the latest results in nonlinear mechanics, obtained recently by the use of a modernized version of Bogoljubov's method of successive changes of variables which ensures rapid convergence.

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Contenuti

0. Introduction.- 1. Quasi-Periodic Solutions in Problems of Nonlinear Mechanics.- § 1. Statement of the Problem. The Existence of an Invariant Manifold.- § 2. Auxiliary Theorems.- § 3. Lemma on Iterations.- § 4. Theorem on Quasi-Periodic Solutions.- § 5. Parametric Dependence of Quasi-Periodic Solutions. Asymptotic and Convergent Expansions.- § 6. Quasi-Periodic Solutions in Second Order Systems.- 2. General Solutions of Nonlinear Differential Equations in the Neighbourhood of Quasi-Periodic Solutions.- § 7. Statement of the Problem.- § 8. Some Auxiliary Statements.- § 9. Inductive Theorem.- § 10. Iteration Process and its Convergence.- § 11. Theorem on Reducibility of Nonlinear Equations.- 3. A Smoothing Technique.- § 12. Loss of Derivatives.- § 13. Examples of Smoothing Operators.- § 14. The Basic Properties of a Smoothing Operator.- § 15. Iteration Process with Smoothing.- 4. Trajectories on a Torus.- § 16. Behaviour of Trajectories on a Two-Dimensional Torus.- § 17. Behaviour of Trajectories on an m-Dimensional Torus.- § 18. Inductive Theorem.- § 19. Proof of the Theorem on the Reducibility of Equations on a Torus.- 5. Linear Systems with Quasi-Periodic Coefficients.- § 20. Reducibility Theorem.- § 21. Solution of the Auxiliary Equation.- § 22. Proof of Reducibility Theorem.- § 23. Construction of a Fundamental Matrix of Solutions.- § 24. The Measure of Reducible Systems. Statement of the Problem.- § 25. A Generalized Reducibility Theorem.- § 26. Metric Propositions.- § 27. Proof of the Measure Theorem.- § 28. Linear Systems with Smooth Right-Hand Sides.- 6. Neighbourhood of an Invariant Smooth Toroidal Manifold.- § 29. Behaviour of Integral Curves in the Neighbourhood of Toroidal Manifolds.- § 30. Auxiliary Propositions.- § 31. Iteration Theorem.- § 32. Reducibility Theorem in the Neighbourhood of a Toroidal Manifold.- § 33. Behaviour under Perturbation of Integral Curves in the Neighbourhood of an Invariant Manifold.- 7. Neighbourhood of a Compact Invariant Manifold of a Non-Autonomous System.- § 34. Statement of the Problem and Basic Postulates.- § 35. Lemma on the Solutions of an Auxiliary System.- § 36. Inductive Theorem.- § 37. Neighbourhood of an Invariant Manifold.- § 38. Behaviour of Solutions of a System of Two Equations in the Neighbourhood of Equilibrium Positions.- Appendices I to XV.- References.

Product Description

Book by Bogoljubov NN Mitropoliskii JA Samoilenko AM

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642619029
• ISBN 13: 9783642619021
• Rilegatura: Copertina flessibile
• Numero di pagine: 300
• Redattore: Sneddon I.N.
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