Preprint A219/2003
Topological dimension of singular-hyperbolic attractors
C. A. Morales
Keywords: Attractor | Partially Hyperbolic | Topological Dimension.
An {\em attractor} is a transitive set of a flow to which all positive orbit close to it converges. An attractor is {\em singular-hyperbolic} if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction \cite{MPP}. The geometric Lorenz attractor \cite{GW} is an example of a singular-hyperbolic attractor with topological dimension $\geq 2$. We shall prove that {\em all} singular-hyperbolic attractors on compact $3$-manifolds have topological dimension $\geq 2$. The proof uses the methods in \cite{MP}.