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arXiv · 1308.3904

The existence of two closed characteristics on every compact star-shaped hypersurface in ${\bf R}^4$

Hui Liu·Yiming Long
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Abstract

Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in ${\bf R}^4$. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et al.

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Hui Liu, Yiming Long. 2014-07-03. The existence of two closed characteristics on every compact star-shaped hypersurface in ${\bf R}^4$. https://arxiv.org/abs/1308.3904

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