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Reversible Polynomial Automorphisms of the Plane: the Involutory Case

A. Gomez·J. D. Meiss
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Abstract

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an involution that is also in the group of polynomial automorphisms. This form is a composition of a sequence of generalized Henon maps together with two simple involutions. We show that the coefficients in the normal form are unique up to finitely many choices.

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A. Gomez, J. D. Meiss. 2002-09-25. Reversible Polynomial Automorphisms of the Plane: the Involutory Case. https://doi.org/10.1016/s0375-9601(03)00605-4

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