关于$\mathbb{R}^{2n}$中某些超曲面上周期轨道的最小数目
On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$
摘要：
我们研究了$\mathbb{R}^{2n}$中非退化动力凸星形超曲面上的周期轨道，沿着Long和Zhu的思路，但是利用了$S^1$ -等变辛同调的性质.证明了在满足最小Conley-Zehnder指数至少为$n-1$的条件下，在$\mathbb{R}^{2n}$中任意非退化星形超曲面上至少存在$n$不同的简单周期轨道.该条件比动力凸性弱。
英文摘要：
We study periodic orbits on a nondegenerate dynamically convex starshaped hypersurface in $\mathbb{R}^{2n}$ along the lines of Long and Zhu, but using properties of the $S^1$-equivariant symplectic homology. We prove that there exist at least $n$ distinct simple periodic orbits on any nondegenerate starshaped hypersurface in $\mathbb{R}^{2n}$ satisfying the condition that the minimal Conley-Zehnder index is at least $n-1$. The condition is weaker than dynamical convexity.
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