Trajectories of a dynamical system determined by a one-parameter group of conformal mappings of \(R^ 3\) (Q796882)

In the three-dimensional space we consider trajectories of a dynamical system generated by a one-parameter group of conformal maps in \(R^ 3\). The systems of this type arise if there exists the first integral linear with respect to the velocity vector in the system of equations of geodesic lines in Riemannian spaces with a conformally flat metric. If the dynamical system has a singular point, it can be linearized by a conformal map. If there are no singular points, we find a family of integral manifolds (tori) around which the trajectories are wound.