论文标题
分析平滑和Nekhoroshev的估计值
Analytic Smoothing and Nekhoroshev estimates for Hölder steep Hamiltonians
论文作者
论文摘要
在本文中，我们证明了Hölder班级中陡峭的汉密尔顿人的Nekhoroshev稳定性的第一个结果。我们的新方法将分析类别中正常形式的经典理论与改进的平滑程序结合在一起，以将HölderHamiltonian近似于分析。仅仅为了清楚起见，我们考虑了可分析性集成的哈密顿式的Hölder扰动的（困难）情况，但是我们的方法足够灵活，可以在包括Gevrey One在内的许多其他功能类别中工作。稳定性指数可以为$（\ ell-1）/（2n {\MathBfα} _1 ... {\MathBfα} _ {n-2}）+1/2 $在稳定性和$ 1/（$ 1/（2N {\MATHBFα} _1 ... _1 ...作为尺寸，$ \ ell> n+1 $是规律性，而$ {\mathbfα} _i $是陡度的指标。获得上述指数的至关重要是对平滑函数的傅立叶规范的一个新的非标准估计。作为副产品，我们改善了$ c^k $类中的稳定性指数，并带有整数$ k $。
In this paper we prove the first result of Nekhoroshev stability for steep Hamiltonians in Hölder class. Our new approach combines the classical theory of normal forms in analytic category with an improved smoothing procedure to approximate an Hölder Hamiltonian with an analytic one. It is only for the sake of clarity that we consider the (difficult) case of Hölder perturbations of an analytic integrable Hamiltonian, but our method is flexible enough to work in many other functional classes, including the Gevrey one. The stability exponents can be taken to be $(\ell-1)/(2n{\mathbfα}_1...{\mathbfα}_{n-2})+1/2$ for the time of stability and $1/(2n{\mathbfα}_1...{\mathbfα}_{n-1})$ for the radius of stability, $n$ being the dimension, $\ell >n+1$ being the regularity and the ${\mathbfα}_i$'s being the indices of steepness. Crucial to obtain the exponents above is a new non-standard estimate on the Fourier norm of the smoothed function. As a byproduct we improve the stability exponents in the $C^k$ class, with integer $k$.
