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On symmetry in periodic solutions of hamiltonian systems

Published online by Cambridge University Press:  09 April 2009

Arthur R. Jones
Arthur R. Jones
Affiliation:
Australian National University, Canberra, A.C.T.
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In this paper the theory of periodic solutions of analytic Hamiltonian systems of differential equations, which is due to Cherry [5], is specialized to systems which have one symmetry property.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 4 , November 1965 , pp. 463 - 486
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Birkhoff, G. D., Dynamical Systems, Amer. Math. Soc. (1927).Google Scholar
[2]Birkhoff, G. D., Collected Mathematical Papers, Amer. Math. Soc. (1950), Vol. I and II.Google Scholar
[3]Cherry, T. M., On the transformation of Hamiltonian systems of linear differential equations with constant or periodic coefficients, Proc. Lond. Math. Soc. 26 (1927), 211–230.CrossRefGoogle Scholar
[4]Cherry, T. M., On the solution of Hamiltonian systems of differential equations in the neighbourhood of a singular point, Proc. Lond. Math. Soc. 27 (1927), 151–170.Google Scholar
[5]Cherry, T. M., On periodic solutions of Hamiltonian systems of differential equations, Phil. Trans. Roy. Soc. A, 227 (1928), 137–221.Google Scholar
[6]De Volgelaere, R., Équation de Hill et problème de Störmer, Canad. Jour. Math. 2 (1950), 440–456.CrossRefGoogle Scholar
[7]De Vogelaere, R., On the structure of symmetric periodic solutions of conservative systems with applications, Contributions to the Theory of Nonlinear Oscillations, IV, Princeton (1958), 53–84.Google Scholar
[8]Moser, J., New aspects in the theory of stability of Hamiltonian systems, Comm. Pure Appl. Math. 11 (1958) 81–114.CrossRefGoogle Scholar
[9]Siegel, C. L., Vorlesungen über Himmelsmechanik, Springer (1956).CrossRefGoogle Scholar
[10]Wintner, A., The Analytical Foundations of Celestial Mechanics, Princeton, (1947).Google Scholar