论文标题
球体上的对称周期性旋转轨道
Symmetric periodic Reeb orbits on the sphere
论文作者
论文摘要
在哈密顿动力学中，长期存在的猜想指出，标准触点领域上的每一个触点表$ s^{2n+1} $至少具有$ n+1 $简单的周期性旋转。在这项工作中，当触点表格具有合适的对称性时，我们考虑了此问题的完善，并且我们询问是否至少有$ n+1 $简单的对称周期性轨道。我们表明，每当接触形式动态凸出时，任何接触形式至少有一个对称周期轨道，至少有两个对称的闭合轨道。
A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the contact form has a suitable symmetry and we ask if there are at least $n+1$ simple symmetric periodic orbits. We show that there is at least one symmetric periodic orbit for any contact form and at least two symmetric closed orbits whenever the contact form is dynamically convex.
