Arnoux-Rauzy Subshifts: Linear Recurrence, Powers, and Palindromes
David Damanik, Luca Q. Zamboni
Abstract
We consider Arnoux-Rauzy subshifts X and study various combinatorial questions: When is X linearly recurrent? What is the maximal power occurring in X? What is the number of palindromes of a given length occurring in X? We present applications of our combinatorial results to the spectral theory of discrete one-dimensional Schrödinger operators with potentials given by Arnoux-Rauzy sequences.
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