Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

Numerical study of periodic Hamiltonian systems by means of associated point mappings


Authors: J. Bernussou and L. Hsu
Journal: Quart. Appl. Math. 34 (1976), 149-171
MSC: Primary 70.65
DOI: https://doi.org/10.1090/qam/451982
MathSciNet review: 451982
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] Raimond A. Struble, Oscillations of a pendulum under parametric excitation, Quart. Appl. Math. 21 (1963), 121–131. MR 0153149, https://doi.org/10.1090/S0033-569X-1963-0153149-4
  • [2] A. Liegeois, Contribution á I'analyse de la stabilité et à la synthése de la commande des satellites contenant des corps en mouvement, Thése de Doctorat és Sciences Physiques, Universite Paul Sabatier, Toulouse (1972)
  • [3] Lucas Pun, Initial conditioned solutions of a second-order nonlinear conservative differential equation with a periodically varying coefficient, J. Franklin Inst. 295 (1973), 193–216. MR 0333366, https://doi.org/10.1016/0016-0032(73)90164-6
  • [4] G. D. Birkhoff, A remark on the dynamical role of Poincaré's last geometric theorem, Collected Mathematical Papers, Dover Inc. 354 (1968)
  • [5] H. Poincare, Les méthodes nouvelles de la mécanique céleste, Gauthier Villars, Paris, 1899
  • [6] G. D. Birkhoff, Surface transformations and their dynamical applications, Coll. Math. Papers, Dover, 113-125 (1968)
  • [7] D. C. Lewis, Formal power series transformations, Duke Math. J. 2, 794 (1939)
  • [8] J. Bernussou, Contribution á létude des solutions des récurrences non linéaires. Application á I'étude de certains systémes á modulation, Thése de Doctorat és Sciences Physiques, Université Paul Sabatier, Toulouse (1974)
  • [9] Carl Ludwig Siegel and Jürgen K. Moser, Lectures on celestial mechanics, Springer-Verlag, New York-Heidelberg, 1971. Translation by Charles I. Kalme; Die Grundlehren der mathematischen Wissenschaften, Band 187. MR 0502448
  • [10] Jean-Pierre Babary and Christian Mira, Sur un cas critique pour une récurrence autonome du deuxième ordre, C. R. Acad. Sci. Paris Sér. A-B 268 (1969), A129–A132 (French). MR 0240488
  • [11] Christian Mira, Étude d’un second cas d’exception pour une récurrence, ou une transformation ponctuelle, autonome du deuxième ordre, à variables réelles, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A332–A335 (French). MR 0254453
    Christian Mira, Sur les cas d’exception d’une récurrence ou une transformation ponctuelle, autonome, du deuxième ordre à variables réelles, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A466–A469 (French). MR 0254454
  • [12] Wolfgang Engel, Ganze Cremona-Transformationen von Primzahlgrad in der Ebene, Math. Ann. 136 (1958), 319–325 (German). MR 0103888, https://doi.org/10.1007/BF01360237
  • [13] L. Hsu, Contribution à l'étude des solutions des récurrences non linéaires. Application aux systémes dynamiques conservatifs, Thése de Doctorat és Sciences Physiques, Université Paul Sabatier, Toulouse (1974)
  • [14] Mathematical methods for digital computers, John Wiley & Sons, Inc., New York-London, 1960. MR 0117906
  • [15] G. D. Birkhoff and P. A. Smith, Structure analysis of surface transformations, Coll. Math. Papers, Dover, 360-394 (1968)
  • [16] B. V. Chirikov, Research concerning the theory of nonlinear resonance and stochasticity, C. E. R. N. Transl. 71-40, Genéve (1971)
  • [17] M. Hénon, Numerical study of some quadratic area-preserving mappings, Quart. Appl. Math. 27, 291-312 (1969)
  • [18] L. J. Laslett, E. M. MacMillan and J. Moser, Long-term stability for particle orbits, Report N. Y. O. 1480-101, New York University (1968)
  • [19] I. Gumowski, Some properties of large amplitude solutions of conservative dynamic systems, CERN/SI/Int. BR/72-1, Genève (1972)
  • [20] Claude Froeschlé and Jean-Paul Scheidecker, Numerical study of the stochasticity of dynamical systems with more than two degrees of freedom, J. Computational Phys. 11 (1973), 423–439. MR 0331749

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 70.65

Retrieve articles in all journals with MSC: 70.65


Additional Information

DOI: https://doi.org/10.1090/qam/451982
Article copyright: © Copyright 1976 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website