Random perturbations and statistical properties of Hénon-like maps

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 ...

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.

Random perturbations of non - uniformly expanding maps ∗

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough. As an application of these results we prove...

Random Perturbations of Non-Uniformly Expanding Maps

Statistical resilience of random populations to random perturbations.

We consider populations represented by random collections of real-valued points, and explore their statistical resilience to random perturbations-seeking populations whose statistics remain qualitatively unchanged by the action of arbitrary random perturbations of a certain type. Studying a general physical perturbation scheme, we obtain an explicit characterization of statistically resilient p...