Expanding maps on 2-step infra-nilmanifolds

A C1-endomorphism f :M→M is expanding if for some Riemannian metric on M there exist c>0, λ>1 such that ∥(Df)mv∥⩾cλm∥v∥ for all v∈TM and all integers m>0. ra-nilmanifold is the quotient of a connected, simply connected nilpotent Lie group G by a discrete cocompact subgroup π of G⋊C, where C is a compact subgroup of Aut(G). The main result is that every 2-step infra-nilmanifold admits an expanding map.