Asymptotic orthogonality of powers of measure-preserving automorphisms and multiplicative functions

An automorphism T is called to have asymptotically orthogonal powers (AOP), if its different prime powers T^p and T^q become closer and closer to be disjoint in the sense of Furstenberg when p,q\to\infty. I will show that the AOP property is achieved in many classical classes of automorphisms, for example: quasi-discrete spectrum automorphisms, nil-rotations and some systems of number theoretic origin. I will also show how the AOP property of uniquely ergodic T is used to show that the observables f(T^{n}x), n\in\N, are orthogonal to any multiplicative arithmetic function u:\N\to\C, |u|\leq1 on so called typical short interval.