We study continuum-wise expansive flows with fixed points on metric spaces and low dimensional manifolds. We give sufficient conditions for a surface flow to be singular cw-expansive and examples showing that cw-expansivity does not imply expansivity. We also construct a singular Axiom A vector field on a three-manifold being singular cw-expansive and with a Lorenz attractor and a Lorenz repeller in its non-wandering set.
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Classical geometric model of the Lorenz attractor.
Topological model of the Lorenz attractor.
The genus two surface S transverse to the flow and containing the Lorenz attractor.
A singular point of the stable foliation appears in