Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in a"e(2n)
Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in a"e(2n)
复制标题
R^{2n} 中非简并星形超曲面的非双曲闭合特性
DOI：
10.1007/s10114-016-6019-9
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发表时间：
2018
影响因子：
0.7
通讯作者：
Wei Wang
中科院分区：
文献类型：
--
作者：
Huagui Duan;Hui Liu;Yiming Long;Wei Wang
本文证明了对于每一个指标完备的非简并紧星形超曲面Σ∧R2n，当其偶时，在Σ上存在至少具有偶Maslovtype指标的非双曲闭特征。当为奇数时，在Σ上存在至少2个马斯洛夫型指标为奇数的闭特征，且至少有（n−1）个闭特征是非双曲的。这里我们称紧星形超曲面Σ∧R2nindex完备，如果它只携带有限多个几何上不同的素数闭特征，并且Σ上的每个素数闭特征（τ,y）都有正的平均指数，且其第一次迭代的maslov型指标（y,m）在n为偶数时满足(y,m)≠−1，当所有m∈n为奇数时满足（y,m）{−2,−1,0}。
In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface Σ ⊂ R2n, there exist at leastnnon-hyperbolic closed characteristics with even Maslovtype indices on Σ whennis even. Whennis odd, there exist at leastnclosed characteristics with odd Maslov-type indices on Σ and at least (n−1) of them are non-hyperbolic. Here we call a compact star-shaped hypersurface Σ ⊂ R2nindex perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic (τ,y) on Σ possesses positive mean index and whose Maslov-type indexi(y,m) of itsm-th iterate satisfiesi(y,m) ≠ −1 when n is even, andi(y,m) ∉ {−2,−1, 0} whennis odd for allm∈ N.