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Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ2n under a pinching condition

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Abstract

In this paper, let Σ ⊂ ℝ2n be a symmetric compact convex hypersurface which is (r, R)-pinched with \(\frac{R} {r} < \sqrt {\frac{5} {3}} \) . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least \(E\left[ {\tfrac{{n - 1}} {2}} \right] + E\left[ {\tfrac{{n - 1}} {3}} \right] \) non-hyperbolic symmetric closed characteristics.

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Authors and Affiliations

  1. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, P. R. China

    Hui Liu

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  1. Hui Liu
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Correspondence to Hui Liu.

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Partially supported by NNSF, RFDP of MOE of China

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Liu, H. Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ2n under a pinching condition. Acta. Math. Sin.-English Ser. 28, 885–900 (2012). https://doi.org/10.1007/s10114-011-0494-9

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  • DOI: https://doi.org/10.1007/s10114-011-0494-9

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