论文标题
在指数稳定的可集成的哈密顿系统的代数性质上
On the algebraic properties of exponentially stable integrable hamiltonian systems
论文作者
论文摘要
陡度是一种几何特性，需要与复杂的分析性，以确保长期以来的近似汉密尔顿系统的稳定性。遵循Nekhoro-Shev制定的策略，我们为给定功能的陡度构建了足够的代数条件，该功能涉及其导数上的代数方程式，直至五个阶。基本分析提出了一些关于陡度的发电性的有趣考虑因素，这是朝着足够条件构建陡峭条件的第一步，涉及所研究功能的衍生物达到任意顺序。
Steepness is a geometric property which, together with complex-analyticity, is needed in order to insure stability of a near-integrable hamiltonian system over exponentially long times. Following a strategy developed by Nekhoro-shev, we construct sufficient algebraic conditions for steepness for a given function that involve algebraic equations on its derivatives up to order five. The underlying analysis suggests some interesting considerations on the gener-icity of steepness and represents a first step towards the construction of sufficient conditions for steepness involving the derivatives of the studied function up to an arbitrary order.
