Abstract
In this article, we discuss subword complexity of colorings of regular trees. We characterize colorings of bounded subword complexity and study Sturmian colorings, which are colorings of minimal unbounded subword complexity. We classify Sturmian colorings using their type sets. We show that any Sturmian coloring is a lifting of a coloring on a quotient graph of the tree which is a geodesic or a ray, with loops possibly attached, thus a lifting of an 'infinite word'. We further give a complete characterization of the quotient graph for eventually periodic colorings.
Original language | English |
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Pages (from-to) | 461-481 |
Number of pages | 21 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 35 |
Issue number | 2 |
DOIs | |
State | Published - 11 Sep 2015 |