TL;DR
This paper investigates singular cw-expansive flows on low-dimensional manifolds, providing conditions for such flows, examples distinguishing cw-expansivity from expansivity, and constructing a singular Axiom A flow with Lorenz attractors.
Contribution
It introduces new conditions for singular cw-expansivity on surfaces and constructs a novel three-manifold flow with Lorenz attractors demonstrating this property.
Findings
Cw-expansivity does not imply expansivity.
Provided sufficient conditions for surface flows to be singular cw-expansive.
Constructed a singular Axiom A flow with Lorenz attractors on a three-manifold.
Abstract
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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