Linearly recurrent subshifts have a finite number of non-periodic subshift factors

Fabien Durand

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arXiv · 0807.4430

Linearly recurrent subshifts have a finite number of non-periodic subshift factors

Fabien Durand

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Abstract

A minimal subshift $(X,T)$ is linearly recurrent if there exists a constant $K$ so that for each clopen set $U$ generated by a finite word $u$ the return time to $U$, with respect to $T$, is bounded by $K|u|$. We prove that given a linearly recurrent subshift $(X,T)$ the set of its non-periodic subshift factors is finite up to isomorphism. We also give a constructive characterization of these subshifts.

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Fabien Durand. 2008-07-28. Linearly recurrent subshifts have a finite number of non-periodic subshift factors. https://arxiv.org/abs/0807.4430

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