@article{8495,
  abstract     = {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 $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-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.},
  author       = {Bounemoura, Abed and Kaloshin, Vadim},
  issn         = {0002-9939},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {4},
  pages        = {1553--1560},
  publisher    = {American Mathematical Society},
  title        = {{A note on micro-instability for Hamiltonian systems close to integrable}},
  doi          = {10.1090/proc/12796},
  volume       = {144},
  year         = {2015},
}