科研之友
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摘要
In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under generic assumptions on h and f, there exists an orbit of the system for which the drift of its action variables is at least of order root epsilon, after a time of order root epsilon(-1). The assumptions, which are essentially minimal, are that there exists a resonant point for h and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting.
- 出版日期2016-4
