In the framework of nonlinear stability of elliptic equilibria in Hamiltonian systems with $ n $ degrees of freedom we provide a criterion to obtain a type of formal stability, called Lie stability. Our result generalises previous approaches, as exponential stability in the sense of Nekhoroshev (excepting a few situations) and other classical results on formal stability of equilibria. In case of Lie stable systems we bound the solutions near the equilibrium over exponentially long times. Some examples are provided to illustrate our main contributions.

中文翻译：

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具有指数时间估计的汉密尔顿系统中椭圆平衡的非线性稳定性

在具有 $n$ 自由度的哈密顿系统中椭圆平衡的非线性稳定性框架中，我们提供了一个标准来获得一种形式稳定性，称为李稳定性。我们的结果概括了以前的方法，如涅霍罗舍夫意义上的指数稳定性（除了少数情况）和其他关于均衡形式稳定性的经典结果。在李稳定系统的情况下，我们在指数长时间内限制平衡附近的解决方案。提供了一些例子来说明我们的主要贡献。