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(1)(y), y' = y + p(2)(x'), where p(1) and p(2) 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. (C) 2002 Michael Baake. Published by Elsevier Science B.V. All rights reserved.