Symbolic discrepancy and self-similar dynamics.
type: Item
instance of: scholarly article
title: Symbolic discrepancy and self-similar dynamics.
zbMATH Open document ID: 1066.11032
author: Boris Adamczewski
publication date: 2005-04-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116172
review text: The author studies symbolic discrepancy for sequences and for subshifts. For infinite sequences (on finite alphabets) this quantity essentially describes how well the sequence sticks to being uniformly distributed with respect to the probability measure naturally associated with this sequence. Without entering into technical details we can comment on one of the main theorems in this paper by saying that the discrepancy of an iterative fixed point of a primitive morphism is governed (for its order of magnitude) by the second eigenvalue of the morphism and its multiplicity, but also -- in some precise cases -- by an explicit complex number depending on the morphism and on the sequence, that is not invariant by abelianization of the morphism.
reviewed by: Jean-Paul Allouche
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 37A30
zbMATH DE Number: 2162454
zbMATH Keywords: discrepancy
zbMATH Keywords: morphisms
zbMATH Keywords: substitutions
zbMATH Keywords: subshifts
zbMATH Keywords: bounded remainder sets
MaRDI profile type: Publication
OpenAlex ID: W200813458
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DOI: 10.5802/AIF.2079
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 2162454