论文标题
对称周期性轨道和三个球体上的截面类似磁盘状的全局表面
Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere
论文作者
论文摘要
我们研究了配备有紧密接触形式和抗接触互动的三个球员上的REEB动力学。我们证明存在对称周期性轨道的存在，并为其提供了必要和足够的条件，以结合截面类似不变的磁盘样的全局表面。我们还研究了在其他对称性的存在下同样的问题，并在这种情况下获得了相似的结果。证明在符号化中利用伪酚形态曲线。作为应用，我们研究了Birkhoff在平面循环限制的三体问题中对磁盘状的截面类似磁盘状的全局表面的猜想，并且在两杆上存在对称封闭的Finsler Geodesics。我们还向某些古典哈密顿系统提供了应用。
We study Reeb dynamics on the three-sphere equipped with a tight contact form and an anti-contact involution. We prove the existence of a symmetric periodic orbit and provide necessary and sufficient conditions for it to bound an invariant disk-like global surface of section. We also study the same questions under the presence of additional symmetry and obtain similar results in this case. The proofs make use of pseudoholomorphic curves in symplectizations. As applications, we study Birkhoff's conjecture on disk-like global surfaces of section in the planar circular restricted three-body problem and the existence of symmetric closed Finsler geodesics on the two-sphere. We also present applications to some classical Hamiltonian systems.
