We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems.
Nous considérons des systèmes dynamiques naturellement associés aux substitutions primitives et connus pour être uniquement ergodiques. Afin d'étudier plus précisément cette propriété, nous introduisons différentes notions de discrépance symbolique. Nous montrons comment les propriétés de répartition d'un tel système sont en partie déterminées par les matrices d'incidences associées à la substitution sous-jacente. Nous donnons également certaines applications de ces résultats à l'étude spectrale des systèmes dynamiques substitutifs.
Keywords: Discrepancy, substitutions, subshifts, bounded remainder sets, self-similar dynamics
Mot clés : discrépance, substitutions, sous-shifts, ensembles à restes bornés, dynamiques auto-similaires
Adamczewski, Boris 1
@article{AIF_2004__54_7_2201_0, author = {Adamczewski, Boris}, title = {Symbolic discrepancy and self-similar dynamics}, journal = {Annales de l'Institut Fourier}, pages = {2201--2234}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2079}, zbl = {1066.11032}, mrnumber = {2139693}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2079/} }
TY - JOUR AU - Adamczewski, Boris TI - Symbolic discrepancy and self-similar dynamics JO - Annales de l'Institut Fourier PY - 2004 SP - 2201 EP - 2234 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2079/ DO - 10.5802/aif.2079 LA - en ID - AIF_2004__54_7_2201_0 ER -
%0 Journal Article %A Adamczewski, Boris %T Symbolic discrepancy and self-similar dynamics %J Annales de l'Institut Fourier %D 2004 %P 2201-2234 %V 54 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2079/ %R 10.5802/aif.2079 %G en %F AIF_2004__54_7_2201_0
Adamczewski, Boris. Symbolic discrepancy and self-similar dynamics. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2201-2234. doi : 10.5802/aif.2079. https://aif.centre-mersenne.org/articles/10.5802/aif.2079/
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