Non-Typical Points for β-Shifts

• Autorzy: Färm D. , Persson T.

Identyfikatory

DOI

10.4064/ba61-2-5

• Języki publikacji: EN

Abstrakty

EN

We study sets of non-typical points under the map fβ↦βx 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.

Słowa kluczowe

EN

beta-shift; non-typical points; Hausdorff dimension

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 2
• Strony: 123--132
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Färm D.

• Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland
• Duvholmsgränd 24 12741 Skärholmen, Sweden

autor

Persson T.

• Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland
• Centre for Mathematical Sciences Lund University Box 118 22100 Lund, Sweden

Bibliografia

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