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

John A.G. Roberts and Michael Baake

Physica A: Statistical Mechanics and its Applications, 2003, vol. 317, issue 1, 95-112

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 formL: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 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.

Keywords: Polynomial automorphism; Symmetry; Reversing symmetry (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:317:y:2003:i:1:p:95-112

DOI: 10.1016/S0378-4371(02)01321-3

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