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arXiv · 0910.2875

A Non-Autonomous Version Of The Denjoy-Wolff Theorem

Tiziano Casavecchia·Santiago Diaz-Madrigal
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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, $ω$-limits formed by suitable closed arcs of circumferences appear now as natural possibilities of asymptotic dynamical behavior.

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Tiziano Casavecchia, Santiago Diaz-Madrigal. 2009-10-15. A Non-Autonomous Version Of The Denjoy-Wolff Theorem. https://arxiv.org/abs/0910.2875

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