Weak mixing and eigenvalues for Arnoux-Rauzy sequences
[Mélange faible et valeurs propres pour les suites d’Arnoux-Rauzy]
Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 1983-2005.

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.

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.

DOI : https://doi.org/10.5802/aif.2403
Classification : 37B10,  68R15
Mots clés : dynamique symbolique, complexité, valeurs propres
@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},
     pages = {1983--2005},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {58},
     number = {6},
     year = {2008},
     doi = {10.5802/aif.2403},
     mrnumber = {2473626},
     zbl = {1151.37013},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2403/}
}
Cassaigne, Julien; Ferenczi, Sébastien; Messaoudi, Ali. Weak mixing and eigenvalues for Arnoux-Rauzy sequences. Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 1983-2005. doi : 10.5802/aif.2403. http://archive.numdam.org/articles/10.5802/aif.2403/

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