The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4 |
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| Authors: | Hui Liu Yi Ming Long |
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| Institution: | 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China;
2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China |
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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 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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| Keywords: | Compact star-shaped hypersurface closed characteristic Hamiltonian systems resonance identity multiplicity |
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