Phase transitions on one-dimensional symbolic systems
By Tamara Kucherenko
Approximating entropy/pressure for multidimensional shifts of finite type
By Ronnie Pavlov
Appears in collections : Combinatorics on words / Combinatoire des mots, Exposés de recherche
We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss further improvements when more assumptions are allowed. This is ongoing work with Michael Damron.