Non-Typical Points for β-Shifts

• Autorzy: David Färm , Tomas Persson
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37C45: Dimension theory of dynamical systems
• 11J83: Metric theory
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 2
• Strony: 123-132

Daty

wydano

2013

Twórcy

autor

David Färm

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

autor

Tomas Persson

• 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

Identyfikatory

DOI

10.4064/ba61-2-5