RESEARCH ARTICLE

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

  • Chungen LIU ,
  • Benxing ZHOU
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  • School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

Received date: 29 Nov 2016

Accepted date: 02 Jan 2017

Published date: 20 Apr 2017

Copyright

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let P ∈ Sp(2n) satisfying Pk = I2n. We consider the minimal Psymmetric period problem of the autonomous nonlinear Hamiltonian system x˙(t)=JH(x(t)). For some symplectic matrices P, we show that for any τ>0, the above Hamiltonian system possesses a periodic solution x with 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).

Cite this article

Chungen LIU , Benxing ZHOU . Minimal P-symmetric period problem of first-order autonomous Hamiltonian systems[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 641 -654 . DOI: 10.1007/s11464-017-0627-2

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