Dynamics of transcendental Hénon maps

Reversible Complex Hénon Maps

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 R2 = U2 = IdC2 . Fixed points and periodic points of order two are classified in terms of symmetry, with respect to R or U , and as either elliptic or saddle points. Orbits are investigated using a Java applet which is provided as an electronic appendix.

Chaotic dynamics of three - dimensional Hénon maps that originate from a homoclinic bifurcation

We study bifurcations of a three-dimensional diffeomorphism, g 0 , that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers (λe iϕ , λe −iϕ , γ), where 0 < λ < 1 < |γ| and |λ 2 γ| = 1. We show that in a three-parameter family, g ε , of dif-feomorphisms close to g 0 , there exist infinitely many open regions near ε = 0 where the corresponding normal form of the fir...

Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map

Three-Dimensional HÉnon-like Maps and Wild Lorenz-like attractors

We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz-type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Hénon map (a simple quadratic map with a constant Jacobian which occurs in a ...

Evolutionary Chaos Controller Synthesis for Stabilizing Chaotic Hénon Maps

This paper deals with synthesizing control laws by means of analytic programming (AP) for the Hénon map, which is a discrete chaotic system. The tool for symbolic regression is used for stabilizing the stable state and higher periodic orbits, which represent oscillations between several values of a chaotic system. For experimentation, the self-organizing migrating algorithm (SOMA) is used with ...