Newtonian Dynamical Systems Admitting Normal Blow-Up of Points

A construction of normal shift along trajectories of a Newtonian dynamical system in the case of an extremely singular initial hypersurface collapsing to a single point is considered. A new class of Newtonian dynamical systems is introduced: systems admitting normal blow-up of points. The class is described in terms of differential equations of normality. Bibliography: 20 titles.