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arXiv · 1605.02242

Perron-Frobenius theory and frequency convergence for reducible substitutions

Martin Lustig·Caglar Uyanik
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Abstract

We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce limit frequencies for factors and hence invariant measures on the associated subshift. The analogous results are well known for primitive substitutions and have found many applications, but for reducible substitutions the tools provided here were so far missing from the theory.

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Martin Lustig, Caglar Uyanik. 2016-05-07. Perron-Frobenius theory and frequency convergence for reducible substitutions. https://doi.org/10.3934/dcds.2017015

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