Symmetries and reversing symmetries of area-preserving polynomial   mappings in generalised standard form
  We determine the symmetries and reversing symmetries within G, the group of real planar polynomial automorphisms, of area-preserving nonlinear polynomial maps L in generalised standard form, L: x'=x+p(y), y'=y+q(x'), where p and q are polynomials. We do this by using the amalgamated free product structure of G. Our results lead to normal forms for polynomial maps in generalised standard form and to a classification of the group structures of the reversing symmetry groups for such maps. 
John A. G. Roberts (UNSW, Sydney) and Michael Baake (Univ. Greifswald)