Periodicity of β-expansions for certain Pisot units*

Vaz, Sandra, and Rodrigues, Pedro Martins. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. "Periodicity of β-expansions for certain Pisot units*." ESAIM: Proceedings 36 (2012): 48-60. <http://eudml.org/doc/251287>.

@article{Vaz2012,
abstract = {Given β > 1, let Tβ\begin\{eqnarray\} T\_\{\beta\}:[0,1[ & \rightarrow& [0,1[ \nonumber\\ \hspace*\{0.5 cm\} x & \rightarrow & \beta x -\lfloor \beta x \rfloor. \nonumber \end\{eqnarray\}The iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β.In [17], K. Schmidt analyzed the set of periodic points of Tβ, where β is a Pisot number. In an attempt to generalize some of his results, we study, for certain Pisot units, a different expansion that we call linear expansion\begin\{eqnarray\} x=\sum\_\{i \geq 0\} e\_i \beta^\{-i\},\nonumber \end\{eqnarray\}where each ei can be superior to  ⌊ β ⌋, its properties and the relation with Per (β).},
author = {Vaz, Sandra, Rodrigues, Pedro Martins},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {beta-expansions; beta-representations; Pisot numbers},
language = {eng},
month = {8},
pages = {48-60},
publisher = {EDP Sciences},
title = {Periodicity of β-expansions for certain Pisot units*},
url = {http://eudml.org/doc/251287},
volume = {36},
year = {2012},
}

TY - JOUR
AU - Vaz, Sandra
AU - Rodrigues, Pedro Martins
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - Periodicity of β-expansions for certain Pisot units*
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 48
EP - 60
AB - Given β > 1, let Tβ\begin{eqnarray} T_{\beta}:[0,1[ & \rightarrow& [0,1[ \nonumber\\ \hspace*{0.5 cm} x & \rightarrow & \beta x -\lfloor \beta x \rfloor. \nonumber \end{eqnarray}The iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β.In [17], K. Schmidt analyzed the set of periodic points of Tβ, where β is a Pisot number. In an attempt to generalize some of his results, we study, for certain Pisot units, a different expansion that we call linear expansion\begin{eqnarray} x=\sum_{i \geq 0} e_i \beta^{-i},\nonumber \end{eqnarray}where each ei can be superior to  ⌊ β ⌋, its properties and the relation with Per (β).
LA - eng
KW - beta-expansions; beta-representations; Pisot numbers
UR - http://eudml.org/doc/251287
ER -