Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form

We determine the symmetries and reversing symmetries within , the group of real planar polynomial automorphisms, of area-preserving nonlinear polynomial maps L in generalised standard form L : x′=x+p1(y), y′=y+p2(x′) ,where p1 and p2 are polynomials. We do this by using the amalgamated free product structure of . 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.