Rational dynamical systems (Q409720)

Let \((X,d)\) be a compact metric space. The author uses the Budak/Isik/Pym representation of rational numbers to extend a family of commuting maps \(\{f_i\}_{i\in\mathbb{Z}^*}\) to \(\{f_i\}_{i\in\mathbb{Q}}\). Finitely many such indexed families of maps that commute are defined to be a rational dynamical system on \(X\). Recurrence properties of such systems are studied; results obtained are in the spirit of the Birkhoff recurrence theorem.