Geometric representation of interval exchange maps over algebraic number fields
Dynamical Systems
2009-11-13 v1
Abstract
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.
Cite
@article{arxiv.0705.1073,
title = {Geometric representation of interval exchange maps over algebraic number fields},
author = {G. Poggiaspalla and J. H. Lowenstein and F. Vivaldi},
journal= {arXiv preprint arXiv:0705.1073},
year = {2009}
}