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Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$

Published 2 Sep 2024 in math.DG and math.DS | (2409.04460v1)

Abstract: In this paper, we proved that for every non-degenerate $C3$ compact star-shaped hypersurface $\Sigma$ in $\mathbb{R}{8}$ which carries no prime closed characteristic of Maslov-type index $-1$, there exist at least four prime closed characteristics on $\Sigma$.

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