Geodesic
Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient
Sbornik. Mathematics, Tome 207 (2016) no. 12, pp. 1709-1728

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Methods are given for the approximate calculation of a branch of a resonance oscillation when it bifurcates from a stationary point and for optimizing this branch with respect to the nonsymmetry coefficient, which is defined as the ratio between the largest and the smallest values of the amplitude. It is shown that the optimal values of the base amplitudes are the coefficients of the corresponding Fejér series. The largest value of the nonsymmetry coefficient is calculated exactly. Bibliography: 18 titles.
Keywords: smooth functional, periodic extremal, nonsymmetry coefficient, Fejér trigonometric series, Lyapunov-Schmidt reduction.
Mots-clés : bifurcation 
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     author = {D. V. Kostin},
     title = {Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient},
     journal = {Sbornik. Mathematics},
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D. V. Kostin. Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient. Sbornik. Mathematics, Tome 207 (2016) no. 12, pp. 1709-1728. http://geodesic.mathdoc.fr/item/SM_2016_207_12_a4/