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Reversible complex Hénon maps. (English) Zbl 1117.32300
Summary: We identify and investigate a class of complex Hénon maps \(H\colon\mathbb C^ 2\rightarrow \mathbb C^ 2\) that are reversible, that is, each \(H\) can be factorized as \(RU\) where \(R^ 2=U^ 2=\text{Id}_{\mathbb C^ 2}\). Fixed points and periodic points of order two and 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 \(H\).

MSC:
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
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