A. A. Azamov, D. Kh. Ruzimuradova, “On the analytic system whose limit set is an unbounded cylinder”, Izv. Vyssh. Uchebn. Zaved. Mat., 2026, Number 2,Pages <nobr>3

On the analytic system whose limit set is an unbounded cylinder

A. A. Azamov, D. Kh. Ruzimuradova

V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, 9 A University str., Tashkent, 100174 Republic of Uzbekistan

Abstract: We consider a problem concerning the topological structure of limit sets of dynamical systems and construct an example of a smooth dynamical system in three-dimensional space whose omega-limit set is an infinite cylinder.

Keywords: dynamical system, invariant cylinder, limit set, density everywhere, Bendixson theorem, irrational rotation of the torus.

UDC: 517.938

Received: 06.09.2024
Revised: 23.11.2024
Accepted: 26.03.2025

DOI: 10.26907/0021-3446-2026-2-3-8