Reversible Complex Hénon Maps

Abstract

We identify and investigate a class of complex Hénon maps H : (C² → C² that are reversible, that is, each H can be factorized as RU where R ² = U ² = Id_C² . Fixed points and periodic points of order two or three are classified in terms of symmetry, with respect to R or U, and as either elliptic or saddle points. We report on experimental investigation, using a Java applet, of the bounded orbits of H.

Keywords:

• Hénon map
• reversibility
• fixed points
• periodic points
• bounded orbits
• ellipticity