论文标题
全球Weinstein型定理有关哈密顿系统的多个旋转周期解决方案
Global Weinstein Type Theorem on Multiple Rotating Periodic Solutions for Hamiltonian Systems
论文作者
论文摘要
本文涉及以$ 2N $尺寸凸汉密尔顿系统的多种旋转周期性解决方案的存在。对于符号正交矩阵$ q $，旋转的周期性解决方案的形式为$ z（t+t）= qz（t）$，根据$ q $的结构，可能是周期性，抗周期性，亚谐波或Quasi-periodic的形式。事实证明，在给定的$ q $不变的凸能表面上，至少存在$ n $几何旋转的周期性解决方案。结果，证明，如果对称能表面允许非对称周期性解决方案，则它具有无限的周期轨道。为了证明结果，我们在旋转周期轨道上引入了一个新的索引。
This paper concerns the existence of multiple rotating periodic solutions for $2n$ dimensional convex Hamiltonian systems. For the symplectic orthogonal matrix $Q$, the rotating periodic solution has the form of $z(t+T)=Qz(t)$, which might be periodic, anti-periodic, subharmonic or quasi-periodic according to the structure of $Q$. It is proved that there exist at least $n$ geometrically distinct rotating periodic solutions on a given $Q$ invariant convex energy surface under a pinching condition. As a result, it is proved that if the symmetric energy surface admits a nonsymmetric periodic solution, it has infinitely many periodic orbits. In order to prove the result, we introduce a new index on rotating periodic orbits.
