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16 February 2025
 
  » arxiv » 1508.0166

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On the minimal number of periodic orbits on some hypersurfaces in $mathbb{R}^{2n}$
Jean Gutt ; Jungsoo Kang ;
Date 1 Aug 2015
AbstractWe 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.
Source arXiv, 1508.0166
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