2 problems

Let $f\in{\mathrm{Homeo}}_0(\mathbb{T}^2)$ have a rotation set $\rho(F)$ with non-empty interior, and let $C\subseteq{\mathrm{int}}(\rho(F))$ be a continuum. A realization conjectu…

Two-fixed-points-or-high-periodic-points conjecture. Either $F$ has two fixed points or $F$ has periodic points of arbitrarily high periods.