On fixed points of maps and iterated maps and applications (Q1582120)

The paper develops results showing that certain continuous maps from the \(n\)-cube \(I^{n}\) into \(\mathbb{R}^{n}\) have periodic points of infinitely many different minimal periods. The assumptions on the map \(f\) are that it is fixed point free, that there are relatively prime integers \(j\) and \(k\) and a set of coordinates \(C\) such that \(0\leq \pi_{i}(f^{j}(x))\leq 1\) and \(0\leq \pi_{i}(f^{k}(x))\leq 1\) for all \(x\in I^{n}\) and \(i\in C\), and that both \(f^{j}\) and \(f^{k}\) satisfy an expansive condition on each coordinate not in \(C\). Some applications to perturbations of the Hénon map, and to an economic model are indicated.