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Mathematische Annalen

, Volume 323, Issue 2, pp 201–215 | Cite as

Multiplicity of closed characteristics on symmetric convex hypersurfaces in $\mathbb{R}^{2n}$

  • Chun-gen Liu
  • Yiming Long
  • Chaofeng Zhu
Original article

Abstract.

Let \(\Sigma\) be a compact \(C^2\) hypersurface in \(\mathbb{R}^{2n}\) bounding a convex set with non-empty interior. In this paper it is proved that there always exist at least n geometrically distinct closed characteristics on \(\Sigma\) if \(\Sigma\) is symmetric with respect to the origin.

Mathematics Subject Classification (2000): 58E05, 70H12, 34C25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Chun-gen Liu
    • 1
  • Yiming Long
    • 2
  • Chaofeng Zhu
    • 2
  1. 1.Department of Mathematics, Nankai University, Tianjin 300071, P. R. of China CN
  2. 2.Nankai Institute of Mathematics, Nankai University, Tianjin 300071, P. R. of China (e-mail: longym@nankai.edu.cn) CN

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