The Periodic Orbit Conjecture for Steady Euler Flows

被引：0
作者：
Robert Cardona
机构：
[1] Universitat Politècnica de Catalunya,Laboratory of Geometry and Dynamical Systems, Department of Mathematics, Barcelona Graduate School of Mathematics (BGSMath)
来源：
Qualitative Theory of Dynamical Systems | 2021年 / 20卷
关键词：
Compact foliations; Smooth dynamics; Euler equations; Geometric currents;
D O I：
暂无
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学科分类号：
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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