On semi-open codes and bi-continuing almost everywhere codes
Dynamical Systems
2015-05-05 v1
Abstract
We will show that a system is synchronized if and only if it has a cover whose cover map is semi-open. Also, any factor code on an irreducible sofic shift is semi-open and the image of a synchronized system by a semi-open code is synchronized. On the other side, right-closing semi-open extension of an irreducible shift of finite type is of finite type. Moreover, we give conditions on finite-to-one factor codes to be open and show that any semi-open code on a synchronized system is bi-continuing a.e.. We give some sufficient conditions for a right-continuing a.e. factor code being right-continuing everywhere.
Keywords
Cite
@article{arxiv.1505.00395,
title = {On semi-open codes and bi-continuing almost everywhere codes},
author = {Dawoud Ahmadi Dastjerdi and Somayyeh Jangjooye Shaldehi},
journal= {arXiv preprint arXiv:1505.00395},
year = {2015}
}