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

By Fabien Durand. Ergodic Theory and Dynamical Systems, 2000

216 citations recorded by the source corpus.

A minimal subshift $(X,T)$ is linearly recurrent (LR) 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 LR 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.

Subfields: Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/eb6a2579a79f043cb9ac6aea8ca3cd01416c8873

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Citations in the corpus

Initial powers of Sturmian sequences (2006, background): “We next show that what we have is indeed an additive S-adic expansion in the sense of [22, 24].”
Dynamics of non-ergodic piecewise affine maps of the torus (2001, background): “[Du] F. Durand.”
Continuous and Measurable Eigenfunctions of Linearly Recurrent Dynamical Cantor Systems (2003, background): “Examples of such systems are substitution subshifts [6] and Sturmian subshifts, whose associated rotation number has a continued fraction with bounded coefficients [4, 5].”
Strictly Ergodic Subshifts and Associated Operators (2005, unknown): “D S] 8 S ep”