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.

中文翻译：

---

稳态Euler流的周期轨道猜想。

周期轨道猜想指出，在闭合流形上，所有消失的矢量场的轨道长度的集合均具有上限，该轨道的所有轨道都是闭合的。由于沙利文（Sullivan）的反例，这种推测通常被认为是错误的。但是，在可测地线的几何条件下是令人满意的。在这项工作中，我们使用Eulerisable流（或更普遍地说，是允许强烈适应一种形式的流）的最新特征来证明这种猜想对于这种更大的向量场仍然成立。