  We study quadratic, volume preserving diffeomorphisms whose inverse is also
quadratic. Such maps generalize the H\'enon area preserving map and the family
of symplectic quadratic maps studied by Moser. In particular, we investigate a
family of quadratic volume preserving maps in three space for which we find a
normal form and study invariant sets. We also give an alternative proof of a
theorem by Moser classifying quadratic symplectic maps.
