Preprint A220/2003
Singular-hyperbolic sets and topological dimension
C. A. Morales
Keywords: Partially Hyperbolic Set | Transitive set | Topological dimension.
A {\it singular-hyperbolic set} for flows is a partially hyperbolic set with singularities (hyperbolic ones) and volume expanding central direction \cite{MPP1}. The class of transitive singular-hyperbolic sets includes the geometric Lorenz attractor and the singular horseshoe \cite{GW, LP}. We prove that all compact, non-singular, invariant subsets of a transitive singular-hyperbolic set are one-dimensional. This generalizes the minimal set's results for Axiom A flows in \cite{B2} to a class of flows studied in \cite{MPP2}.