Analysis seminar

Friday, July 12, 2013 3:30 pm - 3:30 pm EDT (GMT -04:00)

Seminar has been cancelled due to sickness.

Nikita Sidorov, The University of Manchester

“The doubling map with asymmetrical holes”

Let T denote the doubling map on the interval [0,1] and let 0 < a < b < 1. Denote by J(a,b) the set of all x in [0, 1] such that the T -orbit of x has an empty intersection with the interval (a, b).
In my talk I am going to give a full description of (a,b) such that J(a,b) is of positive Hausdorff dimension. This description will involve balanced words and Sturmian sequences. I will also explain how this family of open dynamical systems provides explicit “routes to chaos” previously observed numerically in conventional dynamical systems.
This talk is based on a recent joint paper with Paul Glendinning.