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2013
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 Dudoladov S. L. Stability Criteria of Equilibrium Resonance Position in Systems Admitting First Integral 1996, vol. 1, no. 2, pp.  77-86 Abstract Systems of smooth differential equations in $\mathbb{R}^4$ are considered, which possess the first integral and for which the origin is a nondegenerate equilibrium position. It is assumed that the linear part of such systems has two pairs of pure imaginary eigenvalues $\pm i\omega_1,\,\pm i\omega_2$. For the given two-frequency problem the stability and instability criteria are istablished in a case when the frequences $\omega_1$ and $\omega_2$ are incommensurable as well as in a case of different resonance correlations between them. These criteria are based on the shape of Poincaré-Dulac normal form of corresponding equations of not more than the third order. Citation: Dudoladov S. L.,  Stability Criteria of Equilibrium Resonance Position in Systems Admitting First Integral, Regular and Chaotic Dynamics, 1996, vol. 1, no. 2, pp. 77-86 DOI:10.1070/RD1996v001n02ABEH000017