Hyper-expansive Homeomorphisms

Abstract

A homeomorphism on a compact metric space is said hyper-expansive if every pair of different compact sets are separated by the homeomorphism in the Hausdorff metric. We characterize such dynamics as those with a finite number of orbits and whose non-wandering set is the union of the repelling and the attracting periodic orbits. We also give a characterization of compact metric spaces admiting hyper-expansive homeomorphisms.