Neil MacVicar (Queen's University)
Date
Friday September 30, 202210:00 am - 11:00 am
Location
Jeffery Hall, Room 422Dynamics, Geometry and Groups Seminar
Friday, September 30th, 2022
Time: 10:00 a.m. Place: Jeffery Hall, Room 422
Speaker: Neil MacVicar (Queen's University)
Title: Multiplicative Invariance in the Complex Plane
Abstract: In the late 60s, Hillel Furstenberg proved results and made conjectures concerning the fractal nature of subsets of the unit interval that are invariant under the map that scales a real number by a positive integer r and then kills the integer part. Since then, these sets have been deeply studied. Considerably less has been said about analogous sets in the complex plane. I will review what is known for the case when r is a positive integer that scales real numbers and then introduce a notion of times b invariance in the plane where b is a Gaussian integer. The fractal dimension of these times b invariant sets will be discussed.