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Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. (English) Zbl 1081.81521

Summary: 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.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
37B10 Symbolic dynamics
39A70 Difference operators
47B39 Linear difference operators
47B80 Random linear operators
47N50 Applications of operator theory in the physical sciences
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