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Symmetry in a certain simple perturbed Hamiltonian system. (English) Zbl 0699.34046

The author studies the system \(x'=f(y)+\mu p(t),y=f(x)+\nu q(t)\) where \(\mu\),\(\nu\) are small positive parameters. Conditions are derived guaranteeing that \(\lim_{t\to \infty}[| x(t)| -| y(t)|]=0\) and \(\limsup [| x(t)| +| y(t)|]<\infty\).
Reviewer: H.Hochstadt

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
70H05 Hamilton’s equations
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References:

[1] Arnold V. I.: Ordinary Differential Equations. (2nd edit.). Nauka, Moscow, 1984
[2] Yoshizawa T.: Stability Theory by Liapunov’s Second Method. Math. Soc. Japan, Tokyo, 1966. · Zbl 0144.10802
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