Invariant curves of quasi-periodic reversible mappings

Nonlinearity

Volumn 18, Issue 2, 2005, Pages 685-701

  Liu, Bin ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14844295779     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/2/012     Document Type: Article

References (16)

1. Arnold V I, Kozlov V V and Neishtadt A I 1993 Mathematical Aspects of Classical and Celestial Mechanics 2nd edn (Berlin: Springer)
2. Jorba A and Villanueva J 1997 On the persistence of lower dimensional invariant tori under quasi-periodic perturbations J. Nonlinear Sci. 7 427-73
3. Lazer A C and McKenna P J 1990 Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis SIAM Rev. 32 537-78
4. Levi M and Moser J 2001 A Lagrangian proof of the invariant curve theorem for twist mappings Smooth Ergodic Theory and its Applications (Seattle, WA, 1999) (Proc. Symp. Pure Math. vol 69) (Providence, RI: American Mathematical Society) pp 733-46
5. Levi M and Zehnder E 1995 Boundedness of solutions for quasiperiodic potentials SIAM J. Math. Anal. 26 1233-56
6. Liu B 1999 Boundedness in asymmetric oscillations J. Math. Anal. Appl. 231 355-73
7. Liu B and Song J 2004 Invariant curves of reversible mappings with small twist Acta Math. Sin. 20 15-24 (Engl. Ser.)
8. Moser J 1965 Combination tones for Duffing's equation Commun. Pure Appl. Math. 18 167-81
9. Moser J 1973 Stable and Random Motions in Dynamical Systems (Princeton, NJ: Princeton University Press)
10. Moser J 1988 A stability theorem for minimal foliations on a torus Ergod. Theory Dynam. Syst. 8 251-81
11. Ortega R 1996 Asymmetric oscillators and twist mappings J. London Math. Soc. 53 325-42
12. Ortega R 1999 Boundedness in a piecewise linear oscillator and a variant of the small twist theorem Proc. Lond. Math. Soc. 79 381-413
13. Ortega R 2001 Invariant curves of mappings with averaged small twist Adv. Nonlinear Studies 1 14-39
14. Sevryuk M B 1986 Reversible Systems (Lecture Notes in Mathematics vol 1211) (Berlin: Springer)
15. Siegel C and Moser J 1997 Lectures on Celestial Mechanics (Berlin: Springer)
16. Zharnitsky V 2000 Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problem Nonlinearity 13 1123-36