On the Structure of Lorenz Maps

Abstract

We study the non-wandering set of C 3 contracting Lorenz maps f with negative Schwarzian derivative. We show that if f doesn't have attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a transitive compact set Λ such that ω f (x) = Λ for a residual set of points x ∈ [0, 1]. We also develop in the context of Lorenz maps the classical theory of spectral decomposition constructed for Axiom A maps by Smale.