Fig. 5

Illustrative examples of the four-interval decomposition of the stroboscopic map \(F_{f}\), as discussed in the two major cases of Proposition 4.3 (for \(n=0\) and \(a_{1}<\vartheta_{\ast}\)). The dynamics of critical initial conditions are shown in light solid black. The blue-colored intervals denote the subset of \(\mathbb {T}\) on which \(F_{f}\) is a translation, whereas green and red denote contraction and expansion, respectively