Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in R^{2n}
Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in R^{2n}
复制标题
R^{2n}中紧凸P循环对称超曲面上的多重P循环对称闭特性
DOI：
10.1007/s11464-020-0885-2
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发表时间：
2020
影响因子：
--
通讯作者：
Zhang Hui
中科院分区：
文献类型：
--
作者：
Liu Hui;Zhang Hui
让k≥2是整数和P是一个2 n×2 n辛正交矩阵满足P ~ k = I_ (2 n)和ker (P ~ j -I_ (2 n)) = 0, 1≤j < k。对于任何紧凑凸超曲面Σ⊂R ~ (2 n)与n≥2 P-cyclic对称的,也就是说,x∈Σ意味着Px∈Σ,我们证明如果Σ(R, R)的R / R <√(2 k + 2) / k,然后至少存在n几何不同P-cyclic对称特征在Σ因广泛的一类矩阵P。
Let k ≥ 2 be an integer and P be a 2n × 2n symplectic orthogonal matrix satisfying P~k = I_(2n) and ker(P~j -I_(2n)) = 0,1 ≤ j < k. For any compact convex hypersurface Σ ⊂ R~(2n) with n ≥ 2 which is P-cyclic symmetric, i.e., x ∈ Σ implies Px ∈ Σ,we prove that if Σ is (r, R)-pinched with R/r < √(2k +2)/k, then there exist at least n geometrically distinct P-cyclic symmetric closed characteristics on Σ for a broad class of matrices P.