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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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