## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Words with complexity constraints

**Speaker:** Julien Cassaigne

**Speaker Info:** CNRS

**Brief Description:**

**Special Note**: **note unusual day**

**Abstract:**

The complexity function p(n) of an infinite word (or of a subshift) counts
the number of finite words of each length that occur in it. Certain
constraints on p(n) imply dynamical properties of the subshift,
e.g. p(n) \leq for some n implies periodicity (Morse and Hedlund),
or limsup p(n)/n < 3 implies unique ergodicity (Boshernitzan).
Here we are mainly interested in constraints on \liminf p(n)/n and
\limsup p(n)/n. We discuss how Rauzy graphs and substitutions may be
used to give explicit descriptions of families of words satisfying such
constraints, or to prove that they cannot be satisfied.

**Date:** Monday, May 16, 2022

**Time:** 3:00pm

**Where:** Lunt 103

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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