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}.