We consider a class of symbolic systems over a finite alphabet which are minimal almost one-to-one extensions of rotations of compact metric monothetic groups and provide computations of their enveloping semigroups that highlight their algebraic structure. We describe the set of idempotents of these semigroups and introduce a classification that can help distinguish between certain such systems having zero topological entropy.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-6,
author = {Rafa\l\ Piku\l a},
title = {On enveloping semigroups of almost one-to-one extensions of minimal group rotations},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {249-262},
zbl = {1275.54026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-6}
}
Rafał Pikuła. On enveloping semigroups of almost one-to-one extensions of minimal group rotations. Colloquium Mathematicae, Tome 126 (2012) pp. 249-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-6/