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arXiv · 1705.02725

The large twist theorem and boundedness of solutions for polynomial potentials with $C^1$ time dependent coefficients

Xiong Li·Bin Liu·Yanmei Sun
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Abstract

In this paper we first prove the so-called large twist theorem, then using it to prove the boundedness of all solutions and the existence of quasi-periodic solutions for Duffing's equation $$ \ddot{x}+x^{2n+1}+\dsum_{i=0}^{2n}p_i(t)x^i=0, $$ where $p_i(t)\in C^1(\mathbb{S}) (n+1\leq i\leq 2n)$ and $p_i(t)\in C^0(\mathbb{S}) (0\leq i\leq n)$ with $\mathbb{S}=\mathbb{R}/\mathbb{Z}$.

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Xiong Li, Bin Liu, Yanmei Sun. 2017-05-08. The large twist theorem and boundedness of solutions for polynomial potentials with $C^1$ time dependent coefficients. https://arxiv.org/abs/1705.02725

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