Non-expansive matrix number systems

19.05.2022 15:15 - 17:15

Kevin Hare (University of Waterloo)

Let \(M\) be an \(d \times d\) matrix and \(\mathcal{D}\) be a set of digits in \(\mathbb{R}^d\).  Consider the set of vectors that are represent base \(M\) with digits \(\mathcal{D}\).  Such systems have a long history of study when \(M\) is an expansive matrix.  That is when all the eigenvalues of \(M\) are strictly greater than one in absolute value.

In this talk we will considered the related (but very different) case when \(M = J_d(1)\),  the Jordan block of dimension \(d\) and eigenvalue value \(1\).

Organiser:

H. Bruin, R. Zweimüller