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Diophantine approxi...
Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
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Li, Bing (author)
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- Persson, Tomas (author)
- Lund University,Lunds universitet,Dynamiska system,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Dynamical systems,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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Wang, Baowei (author)
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Wu, Jun (author)
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(creator_code:org_t)
- 2013-09-20
- 2014
- English.
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 276:3-4, s. 799-827
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Abstract
Subject headings
Close
- We consider the distribution of the orbits of the number 1 under the -transformations as varies. Mainly, the size of the set of for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. The dimension of the following set is determined, where is a given point in and is a sequence of integers tending to infinity as . For the proof of this result, the notion of the recurrence time of a word in symbolic space is introduced to characterise the lengths and the distribution of cylinders (the set of with a common prefix in the expansion of 1) in the parameter space .
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- beta-expansion
- Diophantine approximation
- Hausdorff dimension
Publication and Content Type
- art (subject category)
- ref (subject category)
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