Symbolic dynamics on free groups

Steven T. Piantadosi

doi:10.3934/dcds.2008.20.725

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2008, Volume 20, Issue 3: 725-738. Doi: 10.3934/dcds.2008.20.725

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Symbolic dynamics on free groups

Steven T. Piantadosi^1,

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

Received: November 30, 2006

Revised: October 31, 2007

Published: August 2008

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Abstract

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.

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

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