On some properties of motions of dynamical systems on compact manifolds

The article considers the motions of dynamical system g^t defined on a topological compact manifold V. It is shown that the set M_1 of non-wandering points with respect to V is the set of central motions M, and the union of all compact minimal sets is everywhere dense in the set M. It is established that for any motion f(t,p), there exists a compact minimal set Ω⊂V with the following property: for all values t_0∈R and every neighborhood E_Ω of the set Ω, the probability that the arc {f(t,p):t∈[t_0,t_1]} of the motion trajectory f(t,p) belongs to the set E_Ω, tends to 1 as t_1→+∞; a similar statement is true for the arc {f(t,p):t∈[〖-t〗_1,t_0]}. All statements of this article can be transferred without any changes to the system g^t defined in a Hausdorff sequentially compact topological space.