Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

Nonsingular Flows with a Twisted Saddle Orbit on Orientable 3-Manifolds

Olga V. Pochinka, Danila D. Shubin

Laboratory of Dynamical Systems and Application, National Research University “Higher School of Economics”, ul. Bolshaya Pecherckaya 25/12, 603155 Nizhny Novgorod, Russia

Abstract: In this paper we consider nonsingular Morse – Smale flows on closed orientable 3-manifolds, under the assumption that among the periodic orbits of the flow there is only one saddle orbit and it is twisted. It is found that any manifold admitting such flows is either a lens space, or a connected sum of a lens space with a projective space, or Seifert manifolds with base sphere and three special layers. A complete topological classification of the described flows is obtained and the number of their equivalence classes on each admissible manifold is calculated.

Keywords: NMS flow, topological classification, Seifer fiber space

MSC: 37D15

Received: 07.10.2024
Accepted: 06.06.2025

Language: English

DOI: 10.1134/S1560354725040161