A note on univoque self-Sturmian numbers

Jean-Paul Allouche

RAIRO - Theoretical Informatics and Applications (2010)

  • 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 1v, 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 42.4 (2010): 659-662. <http://eudml.org/doc/92895>.

@article{Allouche2010,
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 β in (1,2) is univoque and self-Sturmian if and only if the β-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},
keywords = {Sturmian sequences; univoque numbers; self-Sturmian numbers.; self-Sturmian numbers; kneading sequences},
language = {eng},
month = {3},
number = {4},
pages = {659-662},
publisher = {EDP Sciences},
title = {A note on univoque self-Sturmian numbers},
url = {http://eudml.org/doc/92895},
volume = {42},
year = {2010},
}

TY - JOUR
AU - Allouche, Jean-Paul
TI - A note on univoque self-Sturmian numbers
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
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 β in (1,2) is univoque and self-Sturmian if and only if the β-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.; self-Sturmian numbers; kneading sequences
UR - http://eudml.org/doc/92895
ER -

References

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