English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper studies geometric and spectral properties of $S$-adic shifts andtheir relation to continued fraction algorithms. These shifts are symbolicdynamical systems obtained by iterating infinitely many substitutions. Purediscrete spectrum for $S$-adic shifts and tiling properties of associated Rauzyfractals are established under a generalized Pisot assumption together with ageometric coincidence condition. These general results extend the scope of thePisot substitution conjecture to the $S$-adic framework. They are applied tofamilies of $S$-adic shifts generated by Arnoux-Rauzy as well as Brunsubstitutions. It is shown that almost all of these shifts have pure discretespectrum. Using $S$-adic words related to Brun's continued fraction algorithm,we exhibit bounded remainder sets and natural codings for almost alltranslations on the two-dimensional torus. Due to the lack of self-similarityproperties present for substitutive systems we have to develop new proofs toobtain our results in the $S$-adic setting.

Geometry, dynamics, and arithmetic of $S$-adic shifts