Open maps between shift spaces
Dynamical Systems
2009-09-24 v1
Abstract
Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when bi-closingness replaces closingness. Properties of open mappings between shift spaces are investigated in detail. In particular, we show that a closing open (or constant-to-one) extension preserves the structure of a sofic shift.
Cite
@article{arxiv.0810.4627,
title = {Open maps between shift spaces},
author = {Uijin Jung},
journal= {arXiv preprint arXiv:0810.4627},
year = {2009}
}
Comments
16 pages, 3 figures; to appear in Ergodic Theory Dynamical Systems