2 problems

Orbit-depth and Melnikov-length conjectures. (i) For any polynomial $F$ and any non-trivial cycle $\gamma$ of $F$, either the depth is unbounded, or it is $1$, or $2$. (ii) For any…

Finiteness conjecture. For any $\gamma$, the torsion-free orbit depth $k$ and the orbit depth $\kappa$ are finite.