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<p>We study the topological properties of flows on the Möbius strip whose lifts to a double cover, which is a cylinder, consist of Hamiltonian flows with Hamiltonian in the form of a Morse function constant on the boundary components. We construct a topological classification of these simple flows with the use of distinguishing graphs formed by rooted trees, which are Reeb graphs. The resulting recursive formula is obtained for finding the number of topologically nonequivalent flows with given number of saddles.</p>

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Topological Structure of Simple Pro-Hamiltonian Flows on the Möbius Strip

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Oleksandr Prishlyak,
  • Serhii Stas’

摘要

We study the topological properties of flows on the Möbius strip whose lifts to a double cover, which is a cylinder, consist of Hamiltonian flows with Hamiltonian in the form of a Morse function constant on the boundary components. We construct a topological classification of these simple flows with the use of distinguishing graphs formed by rooted trees, which are Reeb graphs. The resulting recursive formula is obtained for finding the number of topologically nonequivalent flows with given number of saddles.