Reversible Polynomial Automorphisms of the Plane: the Involutory Case

Details Reversible Polynomial Automorphisms of the Plane: the Involutory Case Reversible Polynomial Automorphisms of the Plane: the Involutory Case

2002-09-25

arxiv.org/abs/nlin/0209055v1

Physics Letters A 312(1-2): 49-58 (2003)

Nonlinear Sciences

Chaotic Dynamics

14 pages in laTeX. No figures

Scientific paper

10.1016/S0375-9601(03)00605-4

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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