A note on univoque self-sturmian numbers

Jean-Paul Allouche

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

  • Volume: 42, Issue: 4, page 659-662
  • ISSN: 0988-3754

Abstract

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We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number β in ( 1 , 2 ) is univoque and self-sturmian if and only if the β -expansion of 1 is of the form 1 v , where v is a characteristic sturmian sequence beginning itself in 1 .

How to cite

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Allouche, Jean-Paul. "A note on univoque self-sturmian numbers." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.4 (2008): 659-662. <http://eudml.org/doc/245511>.

@article{Allouche2008,
abstract = {We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number $\beta $ in $(1,2)$ is univoque and self-sturmian if and only if the $\beta $-expansion of $1$ is of the form $1v$, where $v$ is a characteristic sturmian sequence beginning itself in $1$.},
author = {Allouche, Jean-Paul},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {sturmian sequences; univoque numbers; self-sturmian numbers; Sturmian sequences; self-Sturmian numbers; kneading sequences},
language = {eng},
number = {4},
pages = {659-662},
publisher = {EDP-Sciences},
title = {A note on univoque self-sturmian numbers},
url = {http://eudml.org/doc/245511},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Allouche, Jean-Paul
TI - A note on univoque self-sturmian numbers
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2008
PB - EDP-Sciences
VL - 42
IS - 4
SP - 659
EP - 662
AB - We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number $\beta $ in $(1,2)$ is univoque and self-sturmian if and only if the $\beta $-expansion of $1$ is of the form $1v$, where $v$ is a characteristic sturmian sequence beginning itself in $1$.
LA - eng
KW - sturmian sequences; univoque numbers; self-sturmian numbers; Sturmian sequences; self-Sturmian numbers; kneading sequences
UR - http://eudml.org/doc/245511
ER -

References

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