On a new method of qualitative investigation of a gravitating system motion stable according to Lagrange

We formulate the basic problems of investigation and ask some questions concerning dynamic systems, the criteria of stability according to Poisson and the periodicity of formal motion and reveal some new properties. The comparative method of a recurrence over time of differential functional space elements is described which helps us to compare the motion with its characteristics, according to their recurrence over time. Some facts on the theory of measurement are presented and a unification of the Poincaré-Caratheodory classic theory of point recurrence is given. General problems are solved and, in conclusion, we give the results.