Arnoux-Rauzy Subshifts: Linear Recurrence, Powers, and Palindromes

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.

17 pages

References in corpus (4)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity
• Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
• Uniform spectral properties of one-dimensional quasicrystals, IV. Quasi-Sturmian potentials