# American Institute of Mathematical Sciences

June  2017, 37(6): 2945-2956. doi: 10.3934/dcds.2017126

## Singular cw-expansive flows

 Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto, Uruguay

Received  September 2016 Revised  January 2017 Published  February 2017

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.

Citation: Alfonso Artigue. Singular cw-expansive flows. Discrete & Continuous Dynamical Systems, 2017, 37 (6) : 2945-2956. doi: 10.3934/dcds.2017126
##### References:

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##### References:
Classical geometric model of the Lorenz attractor.
Topological model of the Lorenz attractor.
The cylinder $B'$ is transverse to the flow.
The genus two surface S transverse to the flow and containing the Lorenz attractor.
A singular point of the stable foliation appears in $G$.
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