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
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R. A. Struble, Oscillations of a pendulum under parametric excitation, Quart . App. Math. 21, 121–131 (1963)
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)
L. Pun, Initial conditioned solutions of a second order nonlinear conservative differential equation with a periodically varying coefficient, J. Franklin Inst. 295, 193–216 (1973)
G. D. Birkhoff, A remark on the dynamical role of Poincaré’s last geometric theorem, Collected Mathematical Papers, Dover Inc. 354 (1968)
H. Poincare, Les méthodes nouvelles de la mécanique céleste, Gauthier Villars, Paris, 1899
G. D. Birkhoff, Surface transformations and their dynamical applications, Coll. Math. Papers, Dover, 113–125 (1968)
D. C. Lewis, Formal power series transformations, Duke Math. J. 2, 794 (1939)
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)
C. L. Siegel and J. K. Moser, Lectures on celestial mechanics, Springer-Verlag, Berlin, Heidelberg, New York, 1971
J. P. Babary, and C. Mira, Sur un cas critique pour une récurrence autonome du deuxiéme ordre, C. R. A. S. Paris 268, série A, 129–132 (1969)
C. Mira, Sur les cas d’exception d’une récurrence ou transformation ponctuelle autonome du deuxiéme ordre, C. R. A. S. Paris 270, série A, 466 (1970)
W. Engel and G. Cremona, Transformationen von Primzahlgrad in der Ebene, Math. Annalen 136, 319–325 (1958)
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)
W. Ralston, Mathematical methods for digital computers, Wiley, 1960, pp. 95–109
G. D. Birkhoff and P. A. Smith, Structure analysis of surface transformations, Coll. Math. Papers, Dover, 360–394 (1968)
B. V. Chirikov, Research concerning the theory of nonlinear resonance and stochasticity, C. E. R. N. Transl. 71–40, Genéve (1971)
M. Hénon, Numerical study of some quadratic area-preserving mappings, Quart. Appl. Math. 27, 291–312 (1969)
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)
I. Gumowski, Some properties of large amplitude solutions of conservative dynamic systems, CERN/SI/Int. BR/72–1, Genève (1972)
C. Froeschle, Numerical study of the stochasticity of dynamical systems with more than two degrees of freedom, J. Computational Physics 11 (1973)
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Article copyright:
© Copyright 1976
American Mathematical Society