Quadratic volume-preserving maps

Abstract. We study quadratic, volume-preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Hénon 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. AMS classification scheme numbers: 34C20, 34C35, 34C37, 58F05, 70H99 1