Hamiltonian systems with widely separated frequencies

Nonlinearity

Volumn 16, Issue 2, 2003, Pages 689-706

  Tuwankotta, J M ^a   Verhulst, F ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242371137     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/2/319     Document Type: Article

References (31)

1. Abraham R and Marsden J E 1987 Foundations of Mechanics (Reading, MA: Benjamin/Cummings)
2. Arnold V I 1978 Mathematical Methods of Classical Mechanics (New York: Springer)
3. Arnold V I, Kozlov V V and Neishtadt A I 1988 Mathematical aspects of classical and celestial mechanics Encyclopedia of Mathematical Sciences vol 3 Dynamical System ed V I Arnold (New York: Springer)
4. Boertjens G J and van Horssen W T 2000 An asymptotic theory for a beam equations with a quadratic perturbation SIAM J. Appl. Math. 60 602-32
5. Broer H W, Chow S N, Kim Y and Vegter G 1993 A normally elliptic Hamiltonian bifurcation ZAMP 44 389-432
6. Broer H W, Chow S N, Kim Y and Vegter G 1995 The Hamiltonian double-zero eigenvalue Fields Inst. Commun. 4 1-19
7. Broer H W, Hoveijn I, Lunter G A and Vegter G 1998 Resonances in a spring-pendulum: algorithms for equivariant singularity theory Nonlinearity 11 1569-605
8. Churchill R C, Kummer M and Rod D L 1983 On averaging, reduction, and symmetry in Hamiltonian systems J. Diff. Eqns 49 359-414
9. Cicogna G and Gaeta G 1999 Symmetry and Perturbation Theory in Nonlinear Dynamics (Lecture Notes in Physics vol 57) (Berlin: Springer)
10. Crommelin D T 2002 Homoclinic dynamics: a scenario for atmospheric ultralow-frequency variability J. Atmos. Sci. 59 1533-49
11. Gaeta G 1999 Poincaré renormalized forms Ann. Inst. H Poincaré 70 461-514
12. Guckenheimer J and Holmes P H 1997 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Appl. Math. Sci. vol 42) (Berlin: Springer)
13. Gelfreich V and Lerman L 2002 Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system Nonlinearity 15 447-57
14. Haller G 1999 Chaos Near Resonance (Appl. Math. Sci. vol 138) (Berlin: Springer)
15. Kevorkian J and Cole J D 1996 Multiple Time Scale and Singular Perturbation Methods (Appl. Math. Sci. vol 114) (Berlin: Springer)
16. Krol M S 1989 On a Galerkin-averaging method for weakly non-linear wave equations Math. Methods Appl. Sci. 11 649-64
17. Krol M S 1990 The method of averaging in partial differential equations PhD Thesis Universiteit Utrecht
18. Langford W F and Zhan K 1999 Interactions of Andonov-Hopf and Bogdanov-Takens bifurcations Fields Inst. Commun. 24 365-83
19. Langford W F and Zhan K 1999 Hopf bifurcations near 0:1 resonance BTNA'98 Proc. ed Chen, Chow and Li (New York: Springer) pp 1-18
20. Nayfeh A H and Mook D T 1979 Nonlinear Oscillations (New York: Wiley-Interscience)
21. Nayfeh S A and Nayfeh A H 1993 Nonlinear interactions between two widely spaced modes-external excitation Int. J. Bif. Chaos 3 417-21
22. Nayfeh A H and Chin C-M 1995 Nonlinear interactions in a parametrically excited system with widely spaced frequencies Nonlin. Dyn. 7 195-216
23. Palacián J and Yanguas F 2000 Reduction of polynomial planar Hamiltonians with quadratic unperturbed part SIAM Rev. 42 671-91
24. Rink B 2001 Symmetry and resonance in periodic FPU chains Commun. Math. Phys. 218 665-85
25. Robinson J C 2001 Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) (Cambridge: Cambridge University Press)
26. Sanders J A 1978 Are higher order resonances really interesting? Celestial Mech. 16 421-40
27. Sanders J A and Verhulst F 1985 Averaging Methods in Nonlinear Dynamical Systems (Appl. Math. Sci. vol 59) (Berlin: Springer)
28. Stroucken A C J and Verhulst F 1987 The Galerkin-averaging method for nonlinear, undamped continuous systems Math. Meth. Appl. Sci. 9 520-49
29. van der Burgh A H P 1975 On the higher order asymptotic approximations for the solutions of the equations of motion of an elastic pendulum J. Sound Vib. 42 463-75
30. Tuwankotta J M and Verhulst F 2000 Symmetry and resonance in hamiltonian system SIAM J. Appl. Math. 61 1369-85
31. Verhulst F 1999 On averaging methods for partial differential equations SPT98 - Symmetry and Perturbation Theory II ed A Degasperis and G Gaeta (Singapore: World Scientific) pp 79-95