Reversible Polynomial Automorphisms of the Plane

We obtain normal forms for reversible polynomial automorphisms (i.e., polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized Hénon normal form of Friedland and Milnor, specialized to the case that the map has a polynomial reversor. We show that each such reversor has finite order, and that for nontrivial, real maps, the reversor has order 2 or 4. The normal forms are shown to be unique up to finitely many choices. We investigate some of the dynamical consequences of reversibility, especially for the case that the reversor is not an involution.