Dynamics of transcendental Hénon maps III: Infinite entropy

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.

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

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 ...