2009/10/15 by Tiziano Casavecchia, Casavecchia, Tiziano, Santiago Díaz‐Madrigal +1
Mathematics · Computer Science · #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.0910.2875
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, ω-limits formed by suitable closed arcs of circumferences appear now as natural possibilities of asymptotic dynamical behavior.