Pseudo-prolongations in the qualitative theory of dynamical systems

Authors

  • Boris S. Kalitine Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

dynamical system, closed set, attraction, prolongation

Abstract

This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.

Author Biography

  • Boris S. Kalitine, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics), docent; professor at the department of analytical economics and econometrics, faculty of economy 

References

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Published

2022-12-16

Issue

No. 3 (2022): Journal of the Belarusian State University. Mathematics and Informatics

Section

Differential Equations and Optimal Control

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How to Cite

[1]
Kalitine, .B.S. 2022. Pseudo-prolongations in the qualitative theory of dynamical systems. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2022), 45–53. DOI:https://doi.org/10.33581/2520-6508-2022-3-45-53.