# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Non-Typical Points for $\beta$-Shifts

### Tom 61 / 2013

Bulletin Polish Acad. Sci. Math. 61 (2013), 123-132 MSC: 37E05, 37C45, 11J83. DOI: 10.4064/ba61-2-5

#### Streszczenie

We study sets of non-typical points under the map $f_\beta \mapsto \beta x$ mod 1 for non-integer $\beta$ 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 $\beta>1.541$ found in the above paper can be removed.

#### Autorzy

• David FärmInstitute of Mathematics
00-956 Warszawa, Poland
and
Duvholmsgränd 24
12741 Skärholmen, Sweden
e-mail
00-956 Warszawa, Poland
and
Centre for Mathematical Sciences
Lund University
Box 118
22100 Lund, Sweden
e-mail

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