Non-Typical Points for β-Shifts

David Färm, and Tomas Persson. "Non-Typical Points for β-Shifts." Bulletin of the Polish Academy of Sciences. Mathematics 61.2 (2013): 123-132. <http://eudml.org/doc/281257>.

@article{DavidFärm2013,
abstract = {We study sets of non-typical points under the map $f_β ↦ β x $ 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.},
author = {David Färm, Tomas Persson},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {-shift; non-typical points; Hausdorff dimension},
language = {eng},
number = {2},
pages = {123-132},
title = {Non-Typical Points for β-Shifts},
url = {http://eudml.org/doc/281257},
volume = {61},
year = {2013},
}

TY - JOUR
AU - David Färm
AU - Tomas Persson
TI - Non-Typical Points for β-Shifts
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2013
VL - 61
IS - 2
SP - 123
EP - 132
AB - We study sets of non-typical points under the map $f_β ↦ β x $ 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.
LA - eng
KW - -shift; non-typical points; Hausdorff dimension
UR - http://eudml.org/doc/281257
ER -