论文标题
关于参数的连续性模量的KAM定理
KAM theorem on modulus of continuity about parameter
论文作者
论文摘要
在本文中，我们研究了哈密顿系统$ h \ left（{y，x，ξ，\ varepsilon} \ right）= \ left \ left \ langle {ω\ left（ξ\ right），y} \ rangle + rangle + \ rangle + \ \ \ \ \ \ \ v varepsilon p p \ p \ left（ $ P $是连续的$ξ$。我们证明，在某些横向条件下，持续不变的托里（Tori）具有与未扰动的托里（Tori）相同的频率，并且频率映射$ω$的凸状条件较弱。作为一个直接应用程序，当扰动$ p $保持与参数$ξ$有关的任意Hölder连续性时，我们证明了KAM定理。还考虑了无限尺寸的情况。据我们所知，这是使用Hölder类型的参数唯一连续性的系统的第一种方法。
In this paper, we study the Hamiltonian systems $ H\left( {y,x,ξ,\varepsilon } \right) = \left\langle {ω\left( ξ\right),y} \right\rangle + \varepsilon P\left( {y,x,ξ,\varepsilon } \right) $, where $ ω$ and $ P $ are continuous about $ ξ$. We prove that persistent invariant tori possess the same frequency as the unperturbed tori, under certain transversality condition and weak convexity condition for the frequency mapping $ ω$. As a direct application, we prove a KAM theorem when the perturbation $P$ holds arbitrary Hölder continuity with respect to parameter $ ξ$. The infinite dimensional case is also considered. To our knowledge, this is the first approach to the systems with the only continuity in parameter beyond Hölder's type.
