Weak mixing and eigenvalues for Arnoux-Rauzy sequences
Annales de l'Institut Fourier, Volume 58 (2008) no. 6, p. 1983-2005

We define by simple conditions two wide subclasses of the so-called Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counter-example to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.

Nous définissons par des condition simples deux larges sous-classes des systèmes dits d’Arnoux-Rauzy ; les membres de la première possèdent la propriété de mélange faible (mesurable), ce qui généralise et améliore un contre-exemple à la conjecture que tous ces systèmes sont des codages de rotations ; ceux de la seconde ont des valeurs propres, ce qui n’était connu jusqu’ici que pour un ensemble très restreint d’exemples.

DOI : https://doi.org/10.5802/aif.2403
Classification:  37B10,  68R15
Keywords: Symbolic dynamics, complexity, eigenvalues
@article{AIF_2008__58_6_1983_0,
     author = {Cassaigne, Julien and Ferenczi, S\'ebastien and Messaoudi, Ali},
     title = {Weak mixing and eigenvalues for Arnoux-Rauzy sequences},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {6},
     year = {2008},
     pages = {1983-2005},
     doi = {10.5802/aif.2403},
     mrnumber = {2473626},
     zbl = {1151.37013},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_6_1983_0}
}
Cassaigne, Julien; Ferenczi, Sébastien; Messaoudi, Ali. Weak mixing and eigenvalues for Arnoux-Rauzy sequences. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 1983-2005. doi : 10.5802/aif.2403. http://www.numdam.org/item/AIF_2008__58_6_1983_0/

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