In general a polynomial diffeomorphism of the plane can be transformed into
a composition of generalized Henon maps. These maps exhibit some of the fa
miliar properties of the quadratic Henon map, including a bounded set of bo
unded orbits and an anti-integrable limit. We investigate in particular the
cubic, area-preserving case, which reduces to two, two-parameter families
of maps. The bifurcations of low period orbits of these maps are discussed
in detail. (C) 2000 Elsevier Science B.V. All rights reserved.