S-adic words, Rauzy fractals, and torus rotations
speaker: Jörg Thuswaldner (University of Leoben)abstract: In the late 1970s Rauzy observed that classical continued fraction expansions can be used to show that Sturmian words are natural codings of rotations on the one-dimensional torus \({\bf T}^1\) (this was originally proved by Morse and Hedlund in a different way). In 1991 Arnoux and Rauzy proposed a class of three letter words (now called Arnoux-Rauzy words) to generalize this result to higher dimensions. Although in the meantime it was shown that there exist examples of Arnoux-Rauzy words that cannot be natural codings of rotations of \({\bf T}^2\), we are able to prove that almost all such words indeed are natural codings of \({\bf T}^2\).
To prove this result we set up a general theory and give criteria for S-adic shifts to be conjugate to torus rotations. We give examples of such shifts defined in terms of Brun's continued fraction algorithm.
timetable:
Thu 13 Jun, 10:30 - 11:20, Aula Dini
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