An analysis of words coming from Chacon's transformation
Dynamical Systems
2019-09-30 v2
Abstract
We analyze finite and infinite words coming from the symbolic version of Chacon's transformation, focusing on distances between such words. Our main result is that if W = 0010 0010 1 0010 ... is the infinite word usually associated with Chacon's transformation, then the Hamming distance between W and any positive shift of W is strictly greater than 2/9; moreover, this bound is sharp. This yields an alternate proof that Chacon's transformation is non-rigid and (using King's weak closure theorem) has trivial centralizer.
Keywords
Cite
@article{arxiv.1909.11880,
title = {An analysis of words coming from Chacon's transformation},
author = {Patrick Bell and Hunter Brumley and Aaron Hill and Nathanael McGlothlin and Maireigh Nicholas and Tofunmi Ogunfunmi},
journal= {arXiv preprint arXiv:1909.11880},
year = {2019}
}