On the computational complexity of Julia sets in the exponential family, David MartÃ-Pete (University of Liverpool)
Location : Online seminar
Monday, 15. February 2021, 16:00 - 17:00
Computer generated images of Julia sets play a crucial role in establishing new results in complex dynamics. Roughly speaking, a subset of a plane is called computable if there is an algorithm that can produce an approximation of this set with arbitrarily high precision. Computational complexity measures how long it takes for such an algorithm to produce an approximation with a given precision. In this talk, we will give an overview of the main results in this research area, and then we will focus on the computability of Julia sets of functions in the exponential family that have an attracting cycle. These include functions for which the Julia set consists of an uncountable collection of unbounded disjoint curves known as a Cantor bouquet. This is a joint work with Artem Dudko (IMPAN).