Dynamical Systems seminar - On the Hausdorff dimension of boundaries of attracting basins of entire maps

Dates

Wednesday, January 24, 2024 - 13:30 to 14:30

Speaker: Leticia Pardo Simón (University of Manchester)

Abstract: Given an entire map f with an attracting cycle, the points that converge under iteration to such cycle form an open set, known as basin of attraction. The boundaries of such basins lie in the Julia set- the locus of chaos- of the map. In this talk we will discuss under which conditions on f such boundaries have Hausdorff dimension strictly larger than one. This is based on work in progress with K. Barański, B. Karpińska, D. Martí-Pete and A.  Zdunik.