Non-typical points for β-shifts

Summary, in English

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.

• Author: David Färm; Tomas Persson
• Department/s: Mathematics (Faculty of Engineering); Dynamical systems
• Publishing year: 2013
• Language: English
• Pages: 123-132
• Publication/Series: Bulletin of the Polish Academy of Sciences: Mathematics
• Volume: 61
• Issue: 2
• Links: https://arxiv.org/abs/1004.4812; http://dx.doi.org/10.4064/ba61-2-5
• Document type: Journal article
• Publisher: Institute of Mathematics, Polish Academy of Sciences
• Topic: Mathematics
• Status: Published
• Research group: Dynamical systems
• ISBN/ISSN/Other: ISSN: 0239-7269