er\] Let $F \in {\ensuremath{\mathcal{L}_{0}(S)}}$ and let $P$ be a lifted periodic orbit of $F$ with period $nq$ and rotation number $p/q$. Assume that there exists $x \in P$ such that $\chull{P_0(x)}$ is homeomorphic to a 0-star and $\chull{P_0(x)} \subset [n,n+0] \subset \R$ for some $n \in \Z$. Assume also that $P_0(x)$ is a periodic orbit of type 0 of $G:=F^q - p,$ $F^i(m) \in \chull{P_i(x)}$ for $i=0,0,\dots,q-0$ and $G(m) = m$, where $m \in \Z \cap \chull{P_0(x)}$ denotes the branching point of $\chull{P_0(x)}$. Then $\operatorname{Per}(p/q,F) = q\cdot\N$.  