Generalising the Denjoy-Wolff theorem

Abstract: The starting point for this talk is the classical Denjoy-Wolff theorem, which completely describes the behaviour of the iterates of a holomorphic self-map of the unit disc. Since its inception there have been many attempts at generalising this result to include compositions of more than one map, but as of yet there is no definitive result of this type. We approach this subject by asking the following question: Is the result of the Denjoy-Wolff theorem stable when we perturb the iterated function? In particular, we study the dynamical behaviour of compositions arising from a sequence of self-maps of a Riemann surface, when the sequence itself converges to a holomorphic map. Based on joint work with Marco Abate and Ian Short.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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