Generalized Henon maps: the cubic diffeomorphisms of the plane
preprintposted on 2006-02-16, 14:59 authored by Holger R. Dullin, J.D. Meiss
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.
- Mathematical Sciences