可微拟凸Hamilton算子的Nekhoroshev估计
Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians
摘要：
利用Nekhoroshev估计给出了关于可积哈密顿系统扰动的一个重要结果，只要系统是解析的且可积哈密尔顿量不太退化，该结果保证了所有解的指数稳定性.在特殊但重要的情况下，后者是准凸的，这些指数估计已推广的马可和Sauzin，如果哈密尔顿是Gevrey正则，使用的方法介绍了Lochak在分析的情况下。在本文中，使用相同的方法，我们将调查的情况下，哈密顿量被假定为只有可微的，它是已知的，指数稳定性并不成立，但尽管如此，我们将证明估计多项式稳定。
英文摘要：
A major result concerning perturbations of integrable Hamiltonian systems is given by Nekhoroshev estimates, which ensures exponential stability of all solutions provided the system is analytic and the integrable Hamiltonian not too degenerate. In the particular but important case where the latter is quasi-convex, these exponential estimates have been generalized by Marco and Sauzin if the Hamiltonian is Gevrey regular, using a method introduced by Lochak in the analytic case. In this paper, using the same approach we will investigate the situation where the Hamiltonian is assumed to be only finitely differentiable, it is known that exponential stability does not hold but nevertheless we will prove estimates of polynomial stability.
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