Let α be a free group automorphism on FN with maximal index and Σα the associated attracting subshift. We prove that there exists an Interval Exchange Transformation on the circle whose coding factorizes onto Σα. In the case when there is an explicit construction of the ℝ-tree associated to α, we construct algorithmically such IET. We conclude by giving examples.
@article{CML_2012__4_4_A1_0,
author = {Xavier Bressaud and Yann Jullian},
title = {Interval exchange transformation extension of a substitution dynamical system},
journal = {Confluentes Mathematici},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {4},
number = {4},
year = {2012},
doi = {10.1142/S1793744212500053},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744212500053/}
}
TY - JOUR AU - Xavier Bressaud AU - Yann Jullian TI - Interval exchange transformation extension of a substitution dynamical system JO - Confluentes Mathematici PY - 2012 VL - 4 IS - 4 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744212500053/ DO - 10.1142/S1793744212500053 LA - en ID - CML_2012__4_4_A1_0 ER -
%0 Journal Article %A Xavier Bressaud %A Yann Jullian %T Interval exchange transformation extension of a substitution dynamical system %J Confluentes Mathematici %D 2012 %V 4 %N 4 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744212500053/ %R 10.1142/S1793744212500053 %G en %F CML_2012__4_4_A1_0
Xavier Bressaud; Yann Jullian. Interval exchange transformation extension of a substitution dynamical system. Confluentes Mathematici, Tome 4 (2012) no. 4. doi : 10.1142/S1793744212500053. https://cml.centre-mersenne.org/articles/10.1142/S1793744212500053/
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