Geometric representation of interval exchange maps over algebraic number fields

Details Geometric representation of interval exchange maps over algebraic number fields Geometric representation of interval exchange maps over algebraic number fields

2007-05-08

arxiv.org/abs/0705.1073v1

Mathematics

Dynamical Systems

34 pages, 8 postscript figures

Scientific paper

10.1088/0951-7715/21/1/009

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.

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