A Non-Autonomous Version Of The Denjoy-Wolff Theorem

Abstract

The aim of this work is to establish the celebrated Denjoy-Wolff Theorem in the context of generalized Loewner chains. In contrast with the classical situation where essentially convergence to a certain point in the closed unit disk is the unique possibility, several new dynamical phenomena appear in this framework. Indeed, $\omega$-limits formed by suitable closed arcs of circumferences appear now as natural possibilities of asymptotic dynamical behavior.