Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in R^(2n)

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 ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i.e.,x∈∑implies Px∈∑,we prove that if ∑ is(r,R)-pinched with R/r<√(2k+2)/k,then there exist at least n geometrically distince P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.

Stability of Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R^(2n) under a Pinching Condition

In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-1/3] non-hyperbolic symmetric closed characteristics.

Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R^8

Let ∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when ∑ carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.

R^(2n)中P循环对称紧星型超曲面上P循环对称闭特征的多重性

设k≥2是正整数,P=e^(2/kπJ),其中J=(0 In-In 0)是标准辛矩阵.在本文中,我们证明,对R^(2n)中任意P循环对称紧星型超曲面Σ,Σ上至少存在一个P循环对称闭特征,其中n≥2;此外,我们给出星型超曲面上存在n个几何不同P循环对称闭特征的一个充分性条件.