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Nonsingular Morse–Smale Flows with Three Periodic Orbits on Orientable \(3\)-Manifolds

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Abstract

The topological equivalence of nonsingular Morse–Smale flows under assumptions of various generality has been considered in many works (see, e.g., [1]–[4]). However, in the case of a small number of periodic orbits, it is possible to significantly simplify the known invariants and, most importantly, bring the classification problem to implementation by describing the admissibility of the obtained invariants. In the recent paper [5], an exhaustive classification of flows with two orbits on any closed \(n\)-manifolds was obtained. The present paper gives a complete topological classification for flows with three periodic orbits on orientable \(3\)-manifolds.

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Funding

This work was supported by the Russian Science Foundation under grant 21-11-00010, except the work on Sec. 3, which was supported by the Laboratory of Dynamical Systems and Applications NRU HSE under the grant of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-1101), and also except the work on Sec. 4, which was carried out (grant no. 21-04-004) in the framework of the 2021–2022 program “Science Foundation of National Research University Higher School of Economics (NRU HSE).”

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Authors and Affiliations

  1. National Research University Higher School of Economics in Nizhny Novgorod, Nizhny Novgorod, 603155, Russia

    O. V. Pochinka

  2. National Research University Higher School of Economics in Nizhny Novgorod, Nizhny Novgorod, 603155, Russia

    D. D. Shubin

Authors
  1. O. V. Pochinka
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  2. D. D. Shubin
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Correspondence to O. V. Pochinka.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 426–443 https://doi.org/10.4213/mzm13466.

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Pochinka, O.V., Shubin, D.D. Nonsingular Morse–Smale Flows with Three Periodic Orbits on Orientable \(3\)-Manifolds. Math Notes 112, 436–450 (2022). https://doi.org/10.1134/S0001434622090127

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  • DOI: https://doi.org/10.1134/S0001434622090127

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