Symmetries and reversing symmetries of polynomial automorphisms of the   plane
  The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and reversing symmetry groups of a given polynomial automorphism. 
Michael Baake (Bielefeld) and John A.G. Roberts (UNSW, Sydney)