Abstract:
We show that contracting Lorenz maps with negative Schwarzian derivative have only one topological attractor. More precisely, if such a map f has no finite attractor (periodic attractors or super-attractors), then there is a transitive compact set such that it is the omega-limit for a residual set of the interval. From the techniques developed to get this we also have a Spectral Decomposition Theory for these Lorenz maps.