About recurrent motions of periodic processesin a sequentially compact topological space

This article is devoted to the study of the properties of recurrent motions of periodic processes defined in a Hausdorff sequentially compact topological space $\Gamma$.
The definition of a recurrent motion of a periodic process is introduced and the main property of the motions is established. This property strictly connects arbitrary motions and recurrent motions in $\Gamma$. Based on this property, it is shown that, in the case of an autonomous process defined in the space $\Gamma$, the classical G. Birkhoff definition of a recurrent motion is equivalent to the definition of a recurrent motion of a periodic process introduced in this article. Besides, it is shown that in $\Gamma,$ the $\omega$- and $\alpha$-limit sets of each motion of an autonomous process are sequentially compact minimal sets.
The main significance of the results obtained in the article is that they actually establish the interrelation between the motions of periodic processes in the space $\Gamma$.