Conjugacies between general contractions

The main aim of this note is to construct topological conjugacies between linear nonautonomous contractions with discrete time. As a consequence, we obtain topological conjugacies between linear and nonlinear nonautonomous contractions. We consider the general case of linear contractions with respect to arbitrary growth rates e-cρ(m). This includes the usual exponential contractions with ρ(m)=m as a very special case. We also consider the case of contractions that are not uniformly stable. In addition, we show that all conjugacies are locally Hölder outside the origin, and locally Hölder everywhere for a large class of growth rates ρ(m).