Minimal <i>P</i>-symmetric period problem of first-order autonomous Hamiltonian systems

doi:10.1007/s11464-017-0627-2

Front. Math. China

2017, Vol. 12

Issue (3) : 641-654 https://doi.org/10.1007/s11464-017-0627-2

RESEARCH ARTICLE

Minimal P-symmetric period problem of first-order autonomous Hamiltonian systems

Chungen LIU(

), Benxing ZHOU

School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

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Abstract

Let P ∈ Sp(2n) satisfying P^k = I₂_n. We consider the minimal Psymmetric period problem of the autonomous nonlinear Hamiltonian system $x ˙ (t) = J H ′ (x (t))$ . For some symplectic matrices P, we show that for any τ>0, the above Hamiltonian system possesses a kτ periodic solution x with kτ being its minimal P-symmetric period provided H satisfies Rabinowitz’s conditions on the minimal period conjecture, together with that H is convex and H(Px) = H(x).

Keywords Maslov P-index relative Morse index minimal P-symmetric period Hamiltonian system

Corresponding Author(s): Chungen LIU

Issue Date: 20 April 2017

Cite this article:

Chungen LIU,Benxing ZHOU. Minimal P-symmetric period problem of first-order autonomous Hamiltonian systems[J]. Front. Math. China, 2017, 12(3): 641-654.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0627-2
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I3/641

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