Reversible Polynomial Automorphisms of the Plane: the Involutory Case
  Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an involution that is also in the group of polynomial automorphisms. This form is a composition of a sequence of generalized Henon maps together with two simple involutions. We show that the coefficients in the normal form are unique up to finitely many choices. 
A. Gomez and J.D. Meiss