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The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4

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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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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China

    Hui Liu

  2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Yi Ming Long

Authors
  1. Hui Liu
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  2. Yi Ming Long
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Corresponding author

Correspondence to Yi Ming Long.

Additional information

The first author is partially supported by China Postdoctoral Science Foundation (Grant No. 2013M540512); the second author is partially supported by NSFC (Grant No. 11131004), MCME, LPMC of MOE of China, Nankai University and BCMIIS of Capital Normal University

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Liu, H., Long, Y.M. The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4 . Acta. Math. Sin.-English Ser. 32, 40–53 (2016). https://doi.org/10.1007/s10114-014-4108-1

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  • DOI: https://doi.org/10.1007/s10114-014-4108-1

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