Averaging Methods in Nonlinear Dynamical Systems

1. Basic Material and Asymptotics
Jan A. Sanders, Ferdinand Verhulst, James Murdock

2. Averaging: the Periodic Case
Jan A. Sanders, Ferdinand Verhulst, James Murdock

3. Methodology of Averaging
Jan A. Sanders, Ferdinand Verhulst, James Murdock

4. Averaging: the General Case
Jan A. Sanders, Ferdinand Verhulst, James Murdock

5. Attraction
Jan A. Sanders, Ferdinand Verhulst, James Murdock

6. Periodic Averaging and Hyperbolicity
Jan A. Sanders, Ferdinand Verhulst, James Murdock

7. Averaging over Angles
Jan A. Sanders, Ferdinand Verhulst, James Murdock

8. Passage Through Resonance
Jan A. Sanders, Ferdinand Verhulst, James Murdock

9. From Averaging to Normal Forms
Jan A. Sanders, Ferdinand Verhulst, James Murdock

10. Hamiltonian Normal Form Theory
Jan A. Sanders, Ferdinand Verhulst, James Murdock

11. Classical (First-Level) Normal Form Theory
Jan A. Sanders, Ferdinand Verhulst, James Murdock

12. Nilpotent (Classical) Normal Form
Jan A. Sanders, Ferdinand Verhulst, James Murdock

13. Higher-Level Normal Form Theory
Jan A. Sanders, Ferdinand Verhulst, James Murdock

14. The History of the Theory of Averaging
Jan A. Sanders, Ferdinand Verhulst, James Murdock

15. A 4-Dimensional Example of Hopf Bifurcation
Jan A. Sanders, Ferdinand Verhulst, James Murdock

16. Invariant Manifolds by Averaging
Jan A. Sanders, Ferdinand Verhulst, James Murdock

17. Some Elementary Exercises in Celestial Mechanics
Jan A. Sanders, Ferdinand Verhulst, James Murdock

18. On Averaging Methods for Partial Differential Equations
Jan A. Sanders, Ferdinand Verhulst, James Murdock

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Keywords: MATHEMATICS / General MAT000000