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on Generic analytic Arnold diffusion in a priori stable systems

The statement

For a real-analytic steep integrable Hamiltonian $h(I)$ with at least three degrees of freedom, is Arnold diffusion present for a generic sufficiently small real-analytic perturbation $H_\varepsilon(I,\theta)=h(I)+\varepsilon f(I,\theta)$ , in the sense that some orbit changes its action by an amount independent of $\varepsilon$ ?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.