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 $\fM$, and  the union of all compact minimal sets is everywhere dense in the set $\fM.$ It is established that for any motion $f(t,p),$ there exists a compact minimal set $\Om\subset V$ with the following property: for all values $t_0\in\R$ and every neighborhood $E_{\Om}$ of the set $\Om,$ the probability that the arc $\{f(t,p)\colon t\in[t_0,t_1]\}$ of the motion trajectory $f(t,p)$ belongs to the set $E_{\Om},$ tends to 1 as $t_1\to+\iy;$ a similar statement is true for the arc $\{f(t,p)\colon t\in[-t_1,t_0]\}.$

All statements of this article can be transferred without any changes to the system $g^t$ defined in a Hausdorff sequentially compact topological space.