Geodesic
Non-Typical Points for $\beta $-Shifts
David Färm 1   ; Tomas Persson 2
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland and Duvholmsgränd 24 12741 Skärholmen, Sweden
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland and Centre for Mathematical Sciences Lund University Box 118 22100 Lund, Sweden
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 123-132 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba61-2-5
Keywords: study sets non typical points under map beta mapsto beta mod non integer beta extend results fund math several directions particular prove sets points whose forward orbit avoid certain cantor sets set points which ergodic averages diverge have large intersection properties observe technical condition beta found above paper removed

David Färm  1   ; Tomas Persson  2

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland and Duvholmsgränd 24 12741 Skärholmen, Sweden
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland and Centre for Mathematical Sciences Lund University Box 118 22100 Lund, Sweden 
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     title = {Non-Typical {Points} for $\beta ${-Shifts}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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David Färm; Tomas Persson. Non-Typical Points for $\beta $-Shifts. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 123-132. doi: 10.4064/ba61-2-5

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