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.
Keywords: Symbolic dynamics, complexity, eigenvalues
Mot 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},
zbl = {1151.37013},
mrnumber = {2473626},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2403/}
}
TY - JOUR AU - Cassaigne, Julien AU - Ferenczi, Sébastien AU - Messaoudi, Ali TI - Weak mixing and eigenvalues for Arnoux-Rauzy sequences JO - Annales de l'Institut Fourier PY - 2008 SP - 1983 EP - 2005 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2403/ DO - 10.5802/aif.2403 LA - en ID - AIF_2008__58_6_1983_0 ER -
%0 Journal Article %A Cassaigne, Julien %A Ferenczi, Sébastien %A Messaoudi, Ali %T Weak mixing and eigenvalues for Arnoux-Rauzy sequences %J Annales de l'Institut Fourier %D 2008 %P 1983-2005 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2403/ %R 10.5802/aif.2403 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2403/
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