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

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

2002-06-10

arxiv.org/abs/math/0206096v1

Physica A 317 (2002) 95 - 112

Mathematics

Dynamical Systems

22 pages

Scientific paper

10.1016/S0378-4371(02)01321-3

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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