On the diophantine properties of λ-expansions

Summary, in English

For and α, we consider sets of numbers x such that for infinitely many n, x is 2−αn -close to some ∑ n i=1 ω i λ i , where ω i ∈{0,1}. These sets are in Falconer’s intersection classes for Hausdorff dimension s for some s such that −(1/α)(log λ /log 2 )≤s≤1/α. We show that for almost all , the upper bound of s is optimal, but for a countable infinity of values of λ the lower bound is the best possible result.

• Author: Tomas Persson; Henry Reeve
• Department/s: Mathematics (Faculty of Engineering); Dynamical systems
• Publishing year: 2013
• Language: English
• Pages: 65-86
• Publication/Series: Mathematika
• Volume: 59
• Issue: 1
• Links: https://arxiv.org/abs/1202.4904; http://dx.doi.org/10.1112/S0025579312001076
• Document type: Journal article
• Publisher: Cambridge University Press
• Topic: Mathematics
• Status: Published
• Research group: Analysis and Dynamics; Dynamical systems
• ISBN/ISSN/Other: ISSN: 0025-5793