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Reversors and Symmetries for Polynomial Automorphisms of the Plane
We obtain normal forms for symmetric and for reversible polynomial
automorphisms (polynomial maps that have polynomial inverses) of the plane. Our
normal forms are based on the generalized \Henon normal form of Friedland and
Milnor. We restrict to the case that the symmetries and reversors are also
polynomial automorphisms. We show that each such reversor has finite-order, and
that for nontrivial, real maps, the reversor has order 2 or 4. The normal forms
are shown to be unique up to finitely many choices. We investigate some of the
dynamical consequences of reversibility, especially for the case that the
reversor is not an involution.Comment: laTeX with 5 figures. Added new sections dealing with symmetries and
an extensive discussion of the reversing symmetry group
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