Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An example of elliptic stability with large parameters: Lamé's equation and the Arnold-Moser-Rüssmann criterion

Authors: G. Pecelli and E. S. Thomas
Journal: Quart. Appl. Math. 36 (1978), 129-140
MSC: Primary 70.34; Secondary 34D20
DOI: https://doi.org/10.1090/qam/502471
MathSciNet review: 502471
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] V. I. Arnold, Kleine Nenner und Stabilitätsprobleme der klassischen Mechanik und der Himmelsmechanik, Uspekhi Mat. Nauk USSR 18, 6, 9-192 (1963) MR 0170705
  • [2] F. M. Arscott, Periodic differential equations, Pergamon, 1964
  • [3] R. Churchill, H. Jurenka and E. Thomas, A note on iso-energetic stability, Int. J. Non-linear Mech. 12, 37-43 (1977) MR 0449082
  • [4] R. Churchill, G. Pecelli, D. Rod, and S. Sakolic, Coexistence of stable and random motion, Rocky Mountain J. Math. 7, 445-456 (1977). MR 0467817
  • [5] N. W. McLachlan, Ordinary non-linear differential equations in engineering and physical sciences, 2nd edition, Clarendon Press, 1956 MR 0093612
  • [6] W. Magnus and S. Winkler, Hill's equation, Interscience Publishers, 1966
  • [7] J. K. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1 (1962) MR 0147741
  • [8] J. G. Proctor and R. A. Struble, Motion of two weakly coupled nonlinear oscillators, Arch. Rat. Mech. Anal. 18, 293-303 (1965) MR 0171974
  • [9] R. M. Rosenberg and C. P. Atkinson, On the natural modes and their stability in non-linear two-degree-of-freedom systems, J. Appl. Mech. 26, 377-385 (1959) MR 0108009
  • [10] H. Rüssmann, Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Annalen 169, 55-72 (1967) MR 0213679
  • [11] E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th edition, Cambridge University Press, 1952 MR 1424469

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 70.34, 34D20

Retrieve articles in all journals with MSC: 70.34, 34D20

Additional Information

DOI: https://doi.org/10.1090/qam/502471
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society