Scale factor duality in quintessence models ?

We consider several kinds of quintessence models in the framework of scale factor duality. We show that this symmetry exists only for a very small number of quintessence potentials. We then apply the duality transformations found to several analytical solutions. It turns out that, in some cases, the presence of the potential allows a smooth connection between the pre- and the post-Big Bang phases. This may be a first step toward the resolution of the singularity problem.