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The three-body general problem is formulated as a problem of geodesictrajectories flows on the Riemannian manifold. It is proved that a curved spacewith local coordinate system allows to detect new hidden symmetries of theinternal motion of a dynamical system and reduce the three-body problem to thesystem of 6\emph{th} order. It is shown that the equivalence of the initialNewtonian three-body problem and the developed representation providescoordinate transformations in combination with the underdetermined system ofalgebraic equations. The latter makes a system of geodesic equations relativeto the evolution parameter, i.e., to the arc length of the geodesic curve,irreversible. Equations of deviation of geodesic trajectories characterizingthe behavior of the dynamical system as a function of the initial parameters ofthe problem are obtained. To describe the motion of a dynamical systeminfluenced by the external regular and stochastic forces, a system ofstochastic equations (SDE) is obtained. Using the system of SDE, a partialdifferential equation of the second order for the joint probabilitydistribution of the momentum and coordinate of dynamical system in the phasespace is obtained. A criterion for estimating the degree of deviation ofprobabilistic current tubes of geodesic trajectories in the phase andconfiguration spaces is formulated. The mathematical expectation of thetransition probability between two asymptotic subspaces is determined takinginto account the multichannel character of the scattering.

Fundamental irreversibility of the classical three-body problem. New approaches and ideas in the study of dynamical systems