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arXiv · 1812.05838

Rotating Quasi-periodic Solutions of Second Order Hamiltonian Systems with Sub-quadratic Potential

Jiamin Xing·Xue Yang·Yong Li
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Abstract

This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such quasi-periodic solutions, we introduce the $\mathcal{Q}(s)$ index which is a development of the well known $S^1$ index. Applying the $\mathcal{Q}(s)$ index, we give an estimate of the number for rotating quasi-periodic orbits with a fixed period.

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Jiamin Xing, Xue Yang, Yong Li. 2018-12-14. Rotating Quasi-periodic Solutions of Second Order Hamiltonian Systems with Sub-quadratic Potential. https://arxiv.org/abs/1812.05838

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