Perturbation Theory for Viscosity Solutions of Hamilton-Jacobi Equations and Stability of Aubry-Mather Sets
Perturbation Theory for Viscosity Solutions of Hamilton-Jacobi Equations and Stability of Aubry-Mather Sets
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DOI：
10.1137/s0036141002405960
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
D. Gomes
中科院分区：
文献类型：
--
作者：
D. Gomes
本文研究了可积哈密顿系统在小扰动下的稳定性，证明了哈密顿-雅可比方程粘性解的Kam/Nekhoroshev理论的弱形式。我们方法的主要优点是，只需要在渐近展开中的有限个项就可以获得一致控制。因此，不存在收敛问题。这些结果的一个应用是证明了丢番图不变环和Aubry-Mather集在小扰动下是稳定的。
In this paper we study the stability of integrable Hamiltonian systems under small perturbations, proving a weak form of the KAM/Nekhoroshev theory for viscosity solutions of Hamilton--Jacobi equations. The main advantage of our approach is that only a finite number of terms in an asymptotic expansion are needed in order to obtain uniform control. Therefore there are no convergence issues involved. An application of these results is to show that Diophantine invariant tori and Aubry--Mather sets are stable under small perturbations.