Symbolic discrepancy and self-similar dynamics

Boris Adamczewski[1]

  • [1] Université Lyon-I, bât Braconnier, Institut Gérard Desargues, CNRS, 21 avenue Claude Bernard, 69622 Villeurbanne Cedex (France)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2201-2234
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Adamczewski, Boris. "Symbolic discrepancy and self-similar dynamics." Annales de l'Institut Fourier 54.7 (2004): 2201-2234. <http://eudml.org/doc/116172>.

@article{Adamczewski2004,
abstract = {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.},
affiliation = {Université Lyon-I, bât Braconnier, Institut Gérard Desargues, CNRS, 21 avenue Claude Bernard, 69622 Villeurbanne Cedex (France)},
author = {Adamczewski, Boris},
journal = {Annales de l'Institut Fourier},
keywords = {Discrepancy; substitutions; subshifts; bounded remainder sets; self-similar dynamics; discrepancy; morphisms},
language = {eng},
number = {7},
pages = {2201-2234},
publisher = {Association des Annales de l'Institut Fourier},
title = {Symbolic discrepancy and self-similar dynamics},
url = {http://eudml.org/doc/116172},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Adamczewski, Boris
TI - Symbolic discrepancy and self-similar dynamics
JO - Annales de l'Institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2201
EP - 2234
AB - 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.
LA - eng
KW - Discrepancy; substitutions; subshifts; bounded remainder sets; self-similar dynamics; discrepancy; morphisms
UR - http://eudml.org/doc/116172
ER -

References

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