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

John A. G. Roberts·Michael Baake
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Abstract

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.

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John A. G. Roberts, Michael Baake. 2002-06-10. Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form. https://doi.org/10.1016/s0378-4371(02)01321-3

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