Email this article On the interrelation of motions of dynamical systems
- Authors: Afanas’ev A.P.1,2,3, Dzyuba S.M.4
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Affiliations:
- Institute for Information Transmission Problems of the Russian Academy of Sciences
- Lomonosov Moscow State University
- Peoples’ Friendship University of Russia (RUDN University)
- Tver State Technical University
- Issue: Vol 27, No 138 (2022)
- Pages: 136-142
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/295008
- DOI: https://doi.org/10.20310/2686-9667-2022-27-138-136-142
- ID: 295008
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Abstract
In the earlier articles by the authors [A.P. Afanasiev, S.M. Dzyuba, “On new properties of recurrent motions and minimal sets of dynamical systems”, Russian Universities Reports. Mathematics, 26:133 (2021), 5-14] and [A.P. Afanasiev, S.M. Dzyuba, “New properties of recurrent motions and limit motions sets of dynamical systems”, Russian Universities Reports. Mathematics, 27:137 (2022), 5-15], there was actually established the interrelation of motions of dynamical systems in compact metric spaces. The goal of this paper is to extend these results to the case of dynamical systems in arbitrary metric spaces. Namely, let Σ , be an arbitrary metric space. In this article, first of all, a new important property is established that connects arbitrary and recurrent motions in such a space. Further, on the basis of this property, it is shown that if the positive (negative) semitrajectory of some motion f (t , p ) located in Σ is relatively compact, then ω - (α -) limit set of the given motion is a compact minimal set. It follows, that in the space Σ , any nonrecurrent motion is either positively (negatively) outgoing or positively (negatively) asymptotic with respect to the corresponding minimal set.
About the authors
Aleksandr P. Afanas’ev
Institute for Information Transmission Problems of the Russian Academy of Sciences; Lomonosov Moscow State University; Peoples’ Friendship University of Russia (RUDN University)
Email: apa@iitp.ru
Doctor of Physics and Mathematics, the Head of the Center for Distributed Computing; Professor; Professor 19 Bolshoy Karetny per., Moscow 127051, Russian Federation; GSP-1, Leninskie Gory, Moscow 119991, Russian Federation; 6 Miklouho-Maclay St., Moscow 117198, Russian Federation
Sergei M. Dzyuba
Tver State Technical University
Email: sdzyuba@mail.ru
Doctor of Physics and Mathematics, Professor of the Information Systems Department 22 Afanasiya Nikitina nab., Tver 170026, Russian Federation
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