arXiv 2103.024812021-03math.DSmath.DG

The periodic orbit conjecture for steady Euler flows

Robert Cardona

备注：: 12 pages, overall improvements, new title and new section 4
发表信息：: Qual. Theory Dyn. Syst. 20, 52 (2021)
DOI：: 10.1007/s12346-021-00490-w

英文摘要：

The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a counterexample by Sullivan. However, it is satisfied under the geometric condition of being geodesible. In this work, we use the recent characterization of Eulerisable flows (or more generally flows admitting a strongly adapted one-form) to prove that the conjecture remains true for this larger class of vector fields.

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