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Dynamical portraits of rational functions

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If you have a question about this talk, please contact Alexis Marchand .

The iteration of rational functions on the Riemann sphere is fundamental in complex dynamics. There is a special class of `postcritically finite’ (or PCF ) rational functions where the behaviour under iteration is encoded by a finite directed graph called a dynamical portrait. The aim of this talk is to explore which dynamical portraits are possible for PCF rational functions and to present some strategies with a combinatorial and topological flavour, including Thurston’s celebrated Topological Characterisation of Rational Functions.

This talk is part of the Junior Geometry Seminar series.

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