Lower bounds of the topological entropy of maps of \(Y\) (Q1814152)

Denote by \(Y\) the space \(\{z\in\mathbb{C}\mid z^ 3\in[0,1]\}\), and let \(\mathcal Y\) be the family of continuous maps of \(Y\) into itself with 0 as a fixed point. A characterization of the set of periods of periodic orbits of \(f\in{\mathcal Y}\), based upon the knowledge of the behaviour of certain periodic orbits, was given by the first author, \textit{I. Llibre} and \textit{M. Misiurewicz} [Periodic orbits of maps of \(Y\), Trans. Am. Math. Soc. 313, 475-538 (1989)]. Knowing the behaviour of those periodic orbits, the authors of the present paper apply the standard techniques of Block- Guckenheimer-Misiurewicz-Young to calculate the best lower bounds of topological entropy for \(f\in{\mathcal Y}\), depending on the set of periods of \(f\).