%0 Journal Article
%T The existence of two closed characteristics on every compact star-shaped hypersurface in ${\bf R}^4$
%A Hui Liu
%A Yiming Long
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1308.3904v2