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Download file# Generalized Henon maps: the cubic diffeomorphisms of the plane

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posted on 16.02.2006, 14:59 by Holger R. Dullin, J.D. MeissIn 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.

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