In general a polynomial automorphism of the plane can be written as a composition
of generalized Henon maps. These maps exhibit some of the familiar properties
of the quadratic Henon map, including a bounded set of bounded 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.
This is a pre-print. The definitive version: DULLIN, H.R. and MEISS, J.D., 2000. Generalized Henon maps: the cubic diffeomorphisms of the plane. Physica D - Nonlinear Phenomena, 143 (1-4), pp.262-289, is available at: http://www.sciencedirect.com/science/journal/01672789.