Abstract:
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 $\Gamma$.
Fulltext:
PDF file (555 kB)