A Gómez and J D Meiss 2004 Nonlinearity 17 975 doi:10.1088/0951-7715/17/3/012
Reversors and symmetries for polynomial automorphisms of the complex plane
A Gómez1,3 and J D Meiss2
Show affiliationsRecommended by M Field
We obtain normal forms for symmetric and reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the complex and real planes. Our normal forms are based on the Hénon normal form of Friedland and Milnor. We restrict ourselves to the case where 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 where the reversor is not an involution.
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Issue 3 (May 2004)
Received 14 October 2003, in final form 11 February 2004
Published 5 March 2004
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Reversors and symmetries for polynomial automorphisms of the complex plane
A Gómez and J D Meiss 2004 Nonlinearity 17 975
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