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- Färm, DavidLund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH (author)
Simultaneously non-convergent frequencies of words in different expansions
- Article/chapterEnglish2011
Publisher, publication year, extent ...
- 2009-12-24
- Springer Science and Business Media LLC,2011
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- LIBRIS-ID:oai:lup.lub.lu.se:42afd002-5a82-4581-bf7c-9991b7348a98
- https://lup.lub.lu.se/record/1925204URI
- https://doi.org/10.1007/s00605-009-0183-2DOI
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- Language:English
- Summary in:English
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- We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points for the frequencies of words in one symbolic space at a time. We show that the dimension is preserved when such sets defined using different maps are intersected. More precisely, it is proven that the dimension of any countable intersection of sets defined by their sets of accumulation for frequencies of words in different expansions, has dimension equal to the infimum of the dimensions of the sets that are intersected. As a consequence, the set of numbers for which the frequencies do not exist has full dimension even after countable intersections. We also prove that this holds for a dense set of non-integer base expansions.
Subject headings and genre
- NATURVETENSKAP Matematik hsv//swe
- NATURAL SCIENCES Mathematics hsv//eng
- Interval map
- Non-typical point
- Hausdorff dimension
- Beta shift
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- Matematik LTHMatematikcentrum (creator_code:org_t)
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- In:Monatshefte für Mathematik: Springer Science and Business Media LLC162:4, s. 409-4270026-92551436-5081
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