The Interrelation of Motions of Dynamical Systems in a Metric Space

The Interrelation of Motions of Dynamical Systems in a Metric Space

It is shown that if the positive (negative) semitrajectory of some motion , located in a metric space , is relatively compact then the - ( -) limit set of that motion is a compact minimal set. It follows that in the space any non-recurrent motion is either positively (negatively) departing or positi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Lobachevskii journal of mathematics 2022-12, Vol.43 (12), p.3414-3419
Hauptverfasser: Afanas’ev, A. P., Dzyuba, S. M.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Metric space
Probability Theory and Stochastic Processes
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:It is shown that if the positive (negative) semitrajectory of some motion , located in a metric space , is relatively compact then the - ( -) limit set of that motion is a compact minimal set. It follows that in the space any non-recurrent motion is either positively (negatively) departing or positively (negatively) asymptotic with respect to the corresponding compact minimal set.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222150033