Thresholds in Complexity

Abstract: A celebrated result of Morse and Hedlund in 1938 established a link between the complexity function associated to a bi-infinite sequence of symbols and the periodicity of that sequence. In this talk we will continue this investigation, looking at when complexity can yield information about a symbolic system. Spoiler alert: it turns out that it can tell us something about the property of loosely Bernoulli.

We will review notation and definitions, go over some past results in this area, and then culminate in a recent result done jointly with Van Cyr, Bryna Kra, and Ayse Sahin.

dynamical systems

Audience: researchers in the topic

Little school dynamics

Series comments: Email dynamics@aimath.org to ask for the Zoom link.