  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.
