Appears in collection : Composition operators and Banach spaces theory / Opérateurs de composition et espaces de Banach

Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark measures and in terms of their inner-outer factorization. In addition, we show that contractive inner functions can be described in terms of certain mixing property of its boundary values. We also present other results on the boundary behavior of contractive inner functions.