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arXiv · 2205.14789

A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $\mathbf{R}^{2n}$

Huagui Duan·Hui Liu·Wenyan Ren
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Abstract

In this paper, we prove that if all closed characteristics on a compact non-degenerate star-shaped hypersurface $\Sigma$ in $\mathbf{R}^{2n}$ are elliptic, then either there exist exactly $n$ geometrically distinct closed characteristics, or there exist infinitely many geometrically distinct closed characteristics.

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Huagui Duan, Hui Liu, Wenyan Ren. 2022-05-29. A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $\mathbf{R}^{2n}$. https://arxiv.org/abs/2205.14789

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