We study sets of non-typical points under the map mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β > 1.541 found in the above paper can be removed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-5,
author = {David F\"arm and Tomas Persson},
title = {Non-Typical Points for $\beta$-Shifts},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {61},
year = {2013},
pages = {123-132},
zbl = {06238609},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-5}
}
David Färm; Tomas Persson. Non-Typical Points for β-Shifts. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 123-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-5/