First-return limiting notions and rings of Sharkovsky functions (Q1047494)

Let \(\prec\) denote the Sharkovsky ordering of the set of positive integers. A function \(f:\mathbb{R}\to\mathbb{R}\) is called a Sharkovsky function provided that if \(f\) has a periodic point of a prime period \(M\) and \(M\prec K\), then \(f\) has also a periodic point of a prime period \(K\). The authors consider functions \(f:\mathbb{R}\to\mathbb{R}\) for which there exists a ring \(\mathcal{R}_f\) of Sharkovsky functions with \(f\in\mathcal{R}_f\).