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Singular cw-expansive flows. (English) Zbl 1454.37044

Summary: 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.

MSC:

37E35 Flows on surfaces
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
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