Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds

摘要

Let G be a connected, simply connected nilpotent Lie group and Gamma G a lattice. We prove that each ergodic diffeomorphism phi(x Gamma) = uA(x)Gamma on the nilmanifold G/Gamma, where u is an element of G and A : G - G is a unipotent automorphism satisfying A(Gamma) = Gamma, enjoys the property of asymptotically orthogonal powers (AOP). Two consequences follow: