Hojman Symmetry Approach for Scalar-Tensor Cosmology
  Scalar-tensor Cosmologies can be dealt under the standard of the Hojman
conservation theorem that allows to fix the form of the coupling $F(\phi)$, of
the potential $V(\phi)$ and to find out exact solutions for related
cosmological models. Specifically, the existence of a symmetry transformation
vector for the equations of motion gives rise to a Hojman conserved quantity on
the corresponding minisuperpace and exact solutions for the cosmic scale factor
$a$ and the scalar field $\phi$ can be achieved. In particular, we take
advantage of the fact that minimally coupled solutions, previously obtained in
the Einstein frame, can be conformally transformed in non-minimally coupled
solutions in the Jordan frame. Some physically relevant examples are worked
out.
