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\documentstyle[12pt]{article}
\begin{document}
\title{ KAM--theory and stability of stationary solutions of restrict 
problems of cosmical dynamics.} 
\author{E.A. Grebenicov (Computing Center RAS, Moscow)\and M. Jakubiak (University of Podlasie, Siedlce, Poland)
\and D. Kozak--Skoworodkin (University of Podlasie, Siedlce, Poland)}
\date{}
\maketitle
The research of stability of hamiltonian system solutions is based on 
classical stability theory and KAM--theory. The connection of classical and 
KAM--theory theorems is necessary [1]. The constructive part of hamiltonian
system stability theory always will demand of realization of Birkhoff's 
canonical transformations, bringing the hamiltonians to normal form. These 
arduous analytical transformations can be executed effectively only at help 
of suitable computer programmes (for example, System "Mathematica" [2]).
The Arnold and Moser theorems [3,4,5] permit to research the Lyapunov's 
stability stationary solutions of hamiltonian systems of 4-h order.

The new cosmical dynamic models (the restrict problems of n>3 bodies [6]) are
described at such help just of systems, one can so use to them the basic 
KAM--theory theorems.

For concrete values n, at help of programme "Mathematica", it founded the 
stationary solutions, it constructed the Birkhoff's transformations and 
it determinated the intervals of stability and instability of stationary 
solutions [7--10].

\begin{thebibliography}{99}
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1999, pp.138--144.
\bibitem{IP9} E. Grebienicov, D. Kozak, M. Jakubiak. The Algebraic Problems
of the Normalization in Hamiltonian Theory, --Moscow: Proceeding of the Second 
International Workshop on Mathematica System in Teaching and Reserch, Siedlce'2000,
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\bibitem{IP10} D. Kozak, M. Jakubiak. The Birkhoff Hamiltonian Normalization Using the 
"Mathematica", --Odessa: Abstracts of "DIFIN--2000", p. 342.
\end{thebibliography}
\end{document}