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arXiv · 1508.00166

On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$

Jean Gutt·Jungsoo Kang
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Abstract

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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Jean Gutt, Jungsoo Kang. 2015-08-01. On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$. https://arxiv.org/abs/1508.00166

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