
StatusThe thesis was presented on the 3 December, 2004Approved by NCAA on the 27 January, 2005 Abstract– 1.24 Mb / in romanian 
In the thesis is considered the system of type s(T) (T C {0,1. 2.3})
Arj
dx(j)/dt=a(j)+ а(j)ха + а(j)хах0 + а(j)хах?х, (j, а, b, y = 1, 2), (1)
where coefficient tensors a(j)ap and a3Qp are symmetrical in lower indexes in which the complete convolution takes place here.
The work is devoted to study of application of Lie algebras of operators and algebras of invariants to investigation of systems (1). The minimal polynomial basis of centroaffine comitants and invariants is built for systems s(0, 3) and s(0,1, 3), the classification of GL(2, R)orbits' dimensions is done for systems s(0, 2) and s(0, 3). the characteristics of Lie algebra, admitted by system (1). are obtained. The generating functions and Hilbert series are built for algebras of unimodular comitants and invariants for system s(0, 3). and the dimension of Krull is found for these algebras.
In present work factorsystems are built for systems s(0,1), s(0, 1, 2) and s(0, 1, 2, 3), as well as first centroaffine invariant integrals for system s(0, 1) and particular centroaffine invariant integrals for system s(1, 2) on nonsingular invariant manifolds of group GL(2, R).