Fibrewise expansive systems

We prove that compact fibred systems, whose fibre maps are (uniformly) open and (uniformly) expansive, and whose fibres are continuous in the Hausdorff metric, admit a topologically equivalent metric with respect to which their fibre maps are (uniformly) expanding in the sense of Ruelle. This extends Coven and Reddyʹs result on expansive maps of compact metric spaces. Finally, we present a family of fibred complex polynomials which are fibrewise expansive but not fibrewise expanding with respect to the natural metric.