Non-typical points for $β$-shifts

Details Non-typical points for $β$-shifts Non-typical points for $β$-shifts

2010-04-27

arxiv.org/abs/1004.4812v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

We study sets of nontypical points under the map $f_\beta \mapsto \beta x $ mod 1, for non-integer $\beta$ and extend our results from [F\"arm, Persson, Schmeling, to appear] in several directions. In particular we prove that sets of points whose forward orbit avoid certain Cantor sets, and set of points for which ergodic averages diverge, have large intersection properties. We remove the technical condition $\beta>1.541$ found in [F\"arm, Persson, Schmeling, to appear].

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