Pseudo-prolongations in the qualitative theory of dynamical systems

B. S. Kalitin

Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2022), pp. 45-53.

Résumé

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.

Détail

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

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