Sergey Dudoladov
119899, Moscow, Vorobyevy gory
M.V.Lomonosov Moscow State University
Publications:
Borisov A. V., Dudoladov S. L.
Kovalevskaya Exponents and Poisson Structures
1999, vol. 4, no. 3, pp. 1320
Abstract
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.

Dudoladov S. L.
Stability Criteria of Equilibrium Resonance Position in Systems Admitting First Integral
1996, vol. 1, no. 2, pp. 7786
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 twofrequency 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 PoincaréDulac normal form of corresponding equations of not more than the third order.
