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# Symbolic dynamics on free groups

• 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.
Mathematics Subject Classification: Primary: 37B10, 37B40; Secondary: 37B50.

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