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arXiv · 1705.08766

The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition

Nina Xue·Xiong Li
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Abstract

In this paper we are concerned with the periodic Hamiltonian system with one degree of freedom, where the origin is a trivial solution. We assume that the corresponding linearized system at the origin is elliptic, and the characteristic exponents of the linearized system are $\pm iω$ with $ω$ be a Diophantine number, moreover if the system is formally linearizable, then it is analytically linearizable. As a result, the origin is always stable in the sense of Liapunov in this case.

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Nina Xue, Xiong Li. 2017-05-24. The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition. https://arxiv.org/abs/1705.08766

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