Tracker fields from nonminimally coupled theory

We extend the concept of quintessence to flat nonminimally coupled scalar-tensor theories of gravity. By means of Noether’s symmetries for the cosmological pointlike Lagrangian $\mathcal{L},$ it is possible to exhibit exact solutions for a class of models depending on a free parameter s. This parameter comes out in the relationship existing between the coupling $F\left(\phi \right)$ and the potential $V\left(\phi \right)$ because of such a symmetry for $\mathcal{L}.$ When inverse power-law potentials are taken into account, a whole family of exact solutions parametrized by such an s is proposed as a class of tracker fields, and some considerations are made about them.