  The three-body general problem is formulated as a problem of geodesic
trajectories flows on the Riemannian manifold. It is proved that a curved space
with local coordinate system allows to detect new hidden symmetries of the
internal motion of a dynamical system and reduce the three-body problem to the
system of 6\emph{th} order. It is shown that the equivalence of the initial
Newtonian three-body problem and the developed representation provides
coordinate transformations in combination with the underdetermined system of
algebraic equations. The latter makes a system of geodesic equations relative
to the evolution parameter, i.e., to the arc length of the geodesic curve,
irreversible. Equations of deviation of geodesic trajectories characterizing
the behavior of the dynamical system as a function of the initial parameters of
the problem are obtained. To describe the motion of a dynamical system
influenced by the external regular and stochastic forces, a system of
stochastic equations (SDE) is obtained. Using the system of SDE, a partial
differential equation of the second order for the joint probability
distribution of the momentum and coordinate of dynamical system in the phase
space is obtained. A criterion for estimating the degree of deviation of
probabilistic current tubes of geodesic trajectories in the phase and
configuration spaces is formulated. The mathematical expectation of the
transition probability between two asymptotic subspaces is determined taking
into account the multichannel character of the scattering.
