Krzysztof Lech (University of Warsaw): "Random quadratic Julia sets" - November 11, 2021

About this video

This talk was part of the Dynamical Systems seminar at the University of Liverpool.

https://www.liverpool.ac.uk/mathematical-sciences/research/pure-mathematics/research/dynamical-systems/seminars/

Abstract: For a sequence (c_n) let us consider compositions of functions z^2 + c_n. The definitions of the Julia and Fatou sets are naturally extended to these families of compositions. We shall discuss some results on the connectedness of random Julia sets. In particular the following setting will be of interest: let c_n be chosen with uniform distribution from a disk of radius R centered at 0. Depending on R, what can we say of a typical Julia set, i.e. is it connected/disconnected/totally disconnected?

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