 Discrete families of automorphisms have the interesting property that they are generated by one mapping. As we have seen above, all automorphisms satisfy \(T_{t_1 +t_2} = T_{t_1}(T_{t_2})\). From this it follows that \(T_n (x) = T^{n}_1 (x)\), that is \(T_n\) is the \(n\)-th iterate of \(T_1\). In this sense \(T_1\) generates \(\{T_t \mid t \in \mathbb{Z}\}\); or, in other words, \(\{T_t \mid t \in \mathbb{Z}\}\) can be ‘reduced’ to \(T_1\). For this reason one often drops the subscript ‘1’, simply calls the map ‘\(T\)’, and writes the dynamical system as the triple \([X, \mu , T]\), where it is understood that \(T = T_1\).