Sergey Dudoladov

119899, Moscow, Vorobyevy gory
M.V.Lomonosov Moscow State University


Borisov A. V., Dudoladov S. L.
Kovalevskaya Exponents and Poisson Structures
1999, vol. 4, no. 3, pp.  13-20
We consider generalizations of pairing relations for Kovalevskaya exponents in quasihomogeneous systems with quasihomogeneous tensor invariants. The case of presence of a Poisson structure in the system is investigated in more detail. We give some examples which illustrate general theorems.
Citation: Borisov A. V., Dudoladov S. L.,  Kovalevskaya Exponents and Poisson Structures, Regular and Chaotic Dynamics, 1999, vol. 4, no. 3, pp. 13-20
Dudoladov S. L.
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

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