Parameter exclusions for Henon-like systems

Marcelo Viana | Luzzatto, Stefano

Keywords: strange attractor | chaotic dynamics | critical point | unimodal map

This survey is a presentation of the arguments in the proof that Hénon-like maps (null) have a strange attractor, with positive Lebesgue probability in the parameter $a$, if the perturbation size $b$ is small enough. We first sketch a \emph{geometric model} of the strange attractor in this context, emphasising some of its key geometrical properties, and then focus on the construction and estimates required to show that this geometric model does indeed occur for many parameter values.

Anexos:

• exc.ps