Stabilisation conjecture for normal form orbits

For every odd integer $t\geqslant 5$, let $(y_n)$ be the normal form orbit of order $t$. The stabilisation conjecture for normal form orbits. The orbit $(y_n)$ stabilises.

Normal forms model the mean-median dynamics near proper active X-points with a prescribed transit time. Stabilisation of every such normal form orbit would imply stabilisation of the corresponding functional orbits near those X-points; the conjecture is presented without a resolution here.