Abstract
In this chapter we shall present a theorem developed by Moser which extends former work by Kolmogorov and Arnold. The problem to be treated contains those of Sects. 3.9 and 5.2, 3 as special cases. As we have seen before, a set of linearly coupled harmonic oscillators can oscillate at certain basic frequencies so that their total motion is a special case of a quasiperiodic motion. In this chapter we shall deal with the important problem whether nonlinearly coupled oscillators can also perform quasiperiodic motion. We also include in this consideration oscillators which by themselves are nonlinear.
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Bibliography
A. N. Kolmogorov: Dokl. Akad. Nauk. USSR 98, 527 (1954)
V. I. Arnol’d: Russ. Math. Surv. 18, 9 (1963)
J. Moser: Math. Ann. 169, 136 (1967)
J. Moser: “Nearly Integrable and Integrable Systems”, in Topics in Nonlinear Dynamics, ed. by S. Jorna (AIP Conf. Proc. 46, 1 1978)
M. V. Berry: “Regular and Irregular Motion”, in Topics in Nonlinear Dynamics, ed. by S. Jorna (AIP Conf. Proc. 46, 16 1978)
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© 1983 Springer-Verlag Berlin Heidelberg
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Haken, H. (1983). Nonlinear Coupling of Oscillators: The Case of Persistence of Quasiperiodic Motion. In: Advanced Synergetics. Springer Series in Synergetics, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45553-7_6
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DOI: https://doi.org/10.1007/978-3-642-45553-7_6
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