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math.DS2007★ 11 cited
Geometric representation of interval exchange maps over algebraic number fields
G. Poggiaspalla, J. H. Lowenstein, F. Vivaldi
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and…
math.DS2007
Scaling dynamics of a cubic interval exchange transformation
J. H. Lowenstein, F. Vivaldi
We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes…