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On Dynamical Systems With One Degree Of Freedom

Published online by Cambridge University Press:  20 November 2018

C. R. Putnam
C. R. Putnam*
Affiliation:
Purdue University
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1. Introduction. Consider the (vector, n-component) system of differential equations

1,

where f(x) is of class C1. Let Ω denote a set of points, x, consisting of unrestricted solution paths x(t), so that the x(t) exist and lie in Ω for — ∞ < t < ∞.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 280 - 283
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Birkhoff, G. D., Dynamical systems (New York, Amer. Math. Soc., 1927).Google Scholar
2. Brown, A. B., Relations between the critical points and curves of a real analytic function of two independent variables, Ann. Math., 31 (1930), 449–456.Google Scholar
3. Hartman, P. and Wintner, A., Integrability in the large and dynamical stability, Amer. J. Math., 65 (1943), 273–278.Google Scholar
4. Liapounoff, A., Problème générale de la stabilité du mouvement, Ann. Math. Studies, no. 17 (Princeton, 1947).Google Scholar
5. Poincaré, H., Sur les courbes définies par une équation différentielle, J. de Math., ser. 3, 7 (1881), 8 (1883), ser. 4 , 1 (1885), 2 (1886).Google Scholar
6. Poincaré, H., Sur le problème des trois corps et les équations de la dynamique, Acta Math., 13 (1890).Google Scholar
7. Putnam, C. R., Stability and almost periodicity in dynamical systems, Proc. Amer. Math. Soc, 5 (1954), 352–356.Google Scholar
8. Wintner, A., The analytical foundations of celestial mechanics (Princeton, 1941).Google Scholar