Differential equations and Optimal control

Pseudo-prolongations in the qualitative theory of dynamical systems

B. S. Kalitin

Belarusian State University, 4 Niezalieznasci Avenue, Minsk 220030, Belarus

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.

Keywords: dynamical system; closed set; attraction; prolongation.

UDC: 517.938:925

Received: 16.03.2022
Revised: 15.11.2022
Accepted: 15.11.2022

DOI: 10.33581/2520-6508-2022-3-45-53