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doi:10.1007/s11464-020-0885-2

Front. Math. China

2020, Vol. 15

Issue (6) : 1155-1173 https://doi.org/10.1007/s11464-020-0885-2

RESEARCH ARTICLE

Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in

ℝ 2 n

Hui LIU(

), Hui ZHANG

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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Abstract

Let k>2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^k = I₂_n and ker(P^j - I_2n) = 0; 1≤j <k: For any compact convex hypersurface $∑ ⊂ ℝ 2 n$ with n≥2 which is P-cyclic symmetric, i.e., $x ∈ ∑$ implies $P x ∈ ∑$ ; we prove that if $∑$ is (r;R)-pinched with $R / r < (2 k + 2) / k$ ,then there exist at least n geometrically distinct P-cyclic symmetric closed characteristics on $∑$ for a broad class of matrices P:

Keywords Compact convex hypersurfaces Hamiltonian system P-cyclic symmetric closed characteristics multiplicity

Corresponding Author(s): Hui LIU

Issue Date: 05 February 2021

Cite this article:

Hui LIU,Hui ZHANG. Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in

ℝ 2 n

[J]. Front. Math. China, 2020, 15(6): 1155-1173.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0885-2
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1155

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