Discontinuity-growth of interval-exchange maps
Discontinuity-growth of interval-exchange maps
For an interval-exchange map $f$, the number of discontinuities $d(f^n)$either exhibits linear growth or is bounded independently of $n$.This dichotomy is used to prove that the group $\mathcal{E}$ of interval-exchanges does not contain distortion elements, givingexamples of groups that do not act faithfully via interval-exchanges. As a further application ofthis …