ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

generalized Euler Poisson equations 1991 MS Classification: not given Chynkulyak, Nataliya Nikolaevna, Institute of Applied Mathematics and Mechanics, DonetskUkraine Orbital stability of the two-parameter set of the periodic solutions of the generalized Euler Poisson equations Investigation of such property of periodic solutions of autonomous systems of differential equations as Lyapunov stability is difficult problem in rare cases it is completed successfully. Using results of V. I. Zubov and Cetaev’s method of construction of Lyapunov’s function form first integrals for the equations of perturbations, A. Ya. Savchenko suggested the algorithm of investigation of the more rough property solutions as the property of their orbital stability. Modification of this algorithm and its us under investigation of the two-parameter set of the periodic solutions (described in terms of elliptic functions of time) of the generalized Euler-Poisson equations will be presented in this report.