 Let $d \ne 0$ be a real number, $s_d\in\N_{\Sho}$ and $f \in {\mathcal{X}_{0}}$. Then there exists a map $F \in {\ensuremath{\mathcal{L}_{0}(S)}}$ such that ${\ensuremath{\operatorname{Rot}_{_{{\ensuremath{\mathbb{R}}}}}}}(F)=\operatorname{Rot}(F)$ is the closed interval with endpoints $0$ and $d$ (i.e., $[c,d]$ or $[d,c]$), $\operatorname{Per}(0,F) = \operatorname{Per^{\circ}}(f)$ and $\operatorname{Per}(F) = \operatorname{Per^{\circ}}(f) \cup M(0,d) \cup \Lambda(d,\operatorname{S\mbox{\tiny\textup{sh}}}(s_d))$.  