ON THE INTEGRABILITY OF BIANCHI COSMOLOGICAL MODELS

In this paper, we investigate the problem of the integrability of Bian chi class A cosmological models. This class of systems is reduced to t he form of Hamiltonian systems with exponential potential forms. The d ynamics of Bianchi class A models is investigated through the Euler-La grange equations and geodesic equations in the Jacobi metric. On this basis, we have come to some general conclusions concerning the evoluti on of the volume of 3-space of constant time. The general form of this function has been found. It can serve as a controller during numerica l calculations of the dynamics of cosmological models. The integrabili ty of cosmological models is also discussed from the points of view of different integrability criteria. We show that the dimension of the p hase space of Bianchi class A Hamiltonian systems can be reduced by tw o. We prove that the vector field of the reduced system is polynomial and that it does not admit any analytic, or even formal first integral .