Geodesic
Bifurcation of the Equilibrium Point in the Critical Case of Two Pairs of Zero Characteristic Roots
Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 45-60.

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A real autonomous system of four differential equations with a small parameter is considered. It is proved that, under a finite number of explicit conditions on the coefficients of the lower order terms in the expansion of the right-hand sides, its two-dimensional invariant torus bifurcates at infinitesimal frequencies for sufficiently small values of the parameter. Such a system describes, in particular, the oscillations of two weakly coupled oscillators with restoring forces of orders $2n-1$ and $2n+1$. 
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V. V. Basov. Bifurcation of the Equilibrium Point in the Critical Case of Two Pairs of Zero Characteristic Roots. Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 45-60. http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a5/

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