Discontinuity growth of interval exchange maps
Dynamical Systems
2008-11-07 v1 Group Theory
Abstract
For an interval exchange map, the number of discontinuities of its iterates either exhibits linear growth or is bounded. This dichotomy is used to prove that the group of interval exchanges does not contain distortion elements, giving examples of groups that do not act faithfully via interval exchanges. As a further application of this dichotomy, a classification of centralizers in the group of interval exchanges is given. This classification of centralizers is used to compute the automorphism group of the interval exchange group.
Keywords
Cite
@article{arxiv.0811.1014,
title = {Discontinuity growth of interval exchange maps},
author = {Christopher F. Novak},
journal= {arXiv preprint arXiv:0811.1014},
year = {2008}
}
Comments
32 pages, 5 figures