Topological dimension of singular-hyperbolic attractors

Details Topological dimension of singular-hyperbolic attractors Topological dimension of singular-hyperbolic attractors

2003-03-20

arxiv.org/abs/math/0303252v1

Mathematics

Dynamical Systems

18 pages, 1 figure

Scientific paper

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}.

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