Various expansive measures for flows (Q1753216)

The paper under review is a very nice work which presents a characterization of countably expansive flows in measure-theoretical terms as in the discrete case. The authors define the notion of countably expansive flows and prove that a homeomorphism of a compact metric space is countable expansive just when its suspension flow is. Apart from that, in this work are presented several examples. A measure-expansive flow which is not countably expansive is constructed. Moreover, a definition for weak expansive measures for flows is presented, too. It is proved that a flow of a compact metric space is countable expansive if and only if it is weak measure-expansive (i.e. every orbit-vanishing measure is weak expansive). It is noticed that unlike the measure-expansive ones, the weak measure-expansive flows may exist on closed surfaces. To finish, it is proved that the integrated flow of a \(C^1\) vector field on a compact smooth manifold is \(C^1\) stably expansive if and only if it is \(C^1\) stably weak measure-expansive.