# A note on univoque self-Sturmian numbers

RAIRO - Theoretical Informatics and Applications (2010)

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

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topAllouche, 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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