6 problems

Stability conjecture. The stability of the quasiperiodic invariant circle and the stability of periodic solutions with $P\approx m/n$ should be the same.

Consider the quasiperiodically forced system arising from a superlattice potential with incommensurate wave numbers $kappa_1$ and $kappa_2$ satisfying a Diophantine condition. Exis…

Right-special-word conjecture. Based on the examples $\sigma=\sqrt{2}$ and $\sigma=\sqrt{3}$, the $(n-1)$-word that branches in two ways coincides with the unique $n$-word starting…

Unique branching conjecture. Exactly one $n$-word in $s(\gamma_\sigma)$ branches in two ways, while every other $n$-word has a unique extension to an $(n+1)$-word, for each…

Word-complexity conjecture. For such trajectories,

Let $f_{\varepsilon}$ be the conformally symplectic dissipative standard map with complex parameter $\varepsilon$, and let the invariant tori be the quasi-periodic invariant circle…