 Given $c,d \in \R$ with $c \le d$ and $s_c, s_d\in\N_{\Sho}$, there exists a map $F \in {\ensuremath{\mathcal{L}_{0}(S)}}$ such that ${\ensuremath{\operatorname{Rot}_{_{{\ensuremath{\mathbb{R}}}}}}}(F) = \operatorname{Rot}(F) = [c,d]$ and $\operatorname{Per}(F) = \Lambda(c,\operatorname{S\mbox{\tiny\textup{sh}}}(s_c)) \cup M(c,d) \cup \Lambda(d,\operatorname{S\mbox{\tiny\textup{sh}}}(s_d))$.  