On the Statistical Attractors and Attracting Cantor Sets for Piecewise Smooth Maps

Abstract

We discuss some aspects of the asymptotic behavior of the forward orbits of most points for piecewise smooth maps of the interval, specially for contracting Lorenz maps. We are particularly interested in the statistical aspects of most orbits, the existence of statistical attractors and how most orbits in the basin of attraction of an attracting Cantor sets approach the attractor.