Quick Search:
Prog. Theor. Phys. Vol. 62 No. 3 (1979) pp. 620-628
A Perturbation Theory of a Quasi-Periodic Motion
— An Asymptotic Expansion Method
—
Akira Itō
Department of Physics, Kyoto University, Kyoto 606
(Received March 17, 1979)
Abstract:
Quasi-periodic motion (QPM) is structurally unstable and a small perturbation cases a transition to qualitatively different states. This problem is investigated by the asymptotic expansion method of Bogoliubov and Mitropolsky. It is shown that the structurally unstable QPM is in a sense “stable”, and has its reality contrary to Ruelle's suggestion.
URL :
http://ptp.ipap.jp/link?PTP/62/620/
DOI : 10.1143/PTP.62.620
References:
- P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiely-Interscience, New York, 1971).
For more recent studies, see papers in Prog. Theor. Phys. Suppl. No. 64 (1978).
- G. Ahlers, preprint.
- E. Hopf, Ber. Math-Phys. Kl. Sächs. Akad. Wiss. Leipzig 94 (1942), 1.
- A. Itō, Prog. Theor. Phys. 61 (1979), 815[PTP].
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1959).
-
D. Ruelle and F. Takens, Commun. Math. Phys. 20 (1971), 167[CrossRef].
- N. N. Bogoliubov and U. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations (Dehli, Hindustan, 1961).
- See, e.g., Moser, Izvestia Akad. Nauk. 25 (1961), 21.
-
J. Sherman and J. McLaughlin, Commun. Math. Phys. 58 (1978), 9[CrossRef].
- T. Yamada and H. Fujisaka, Z. Phys. B 28 (1977), 239.
- H. Kidachi, preprint.
- A. Itō, Prog. Theor. Phys. 61 (1979), 45[PTP].
- K. Tomita and T. Kai, Prog. Theor. Phys. 61 (1979), 54[PTP].
