# American Institute of Mathematical Sciences

July  2008, 20(3): 725-738. doi: 10.3934/dcds.2008.20.725

## Symbolic dynamics on free groups

 1 Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, NC 27599, United States

Received  December 2006 Revised  November 2007 Published  December 2007

We study nearest-neighbor shifts of finite type (NNSOFT) on a free group $\G$. We determine when a NNSOFT on $\G$ admits a periodic coloring and give an example of a NNSOFT that does not allow a periodic coloring. Then, we find an expression for the entropy of the golden mean shift on $\G$. In doing so, we study a new generalization of Fibonacci numbers and analyze their asymptotics with a one-dimensional iterated map that is related to generalized continued fractions.
Citation: Steven T. Piantadosi. Symbolic dynamics on free groups. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 725-738. doi: 10.3934/dcds.2008.20.725
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