Rational functions are not very useful for obtaining global differential mo
dels because they involve poles that may eject the trajectory to infinity.
In contrast, it is here shown that they allow one to significantly improve
the quality of models for maps. In such a case, the presence of poles does
not involve any numerical difficulty when the models are iterated. The mode
ls then take advantage of the ability of rational functions to capture comp
licated structures that may be generated by maps. The method is applied to
experimental data from copper electrodissolution.