Abstract
Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in ℝ4. 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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