Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions

Summary, in English

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 .

• Författare: Bing Li; Tomas Persson; Baowei Wang; Jun Wu
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2014
• Språk: Engelska
• Sidor: 799-827
• Publikation/Tidskrift/Serie: Mathematische Zeitschrift
• Volym: 276
• Issue: 3-4
• Länkar: https://arxiv.org/abs/1301.3595; http://dx.doi.org/10.1007/s00209-013-1223-0
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Nyckelord: beta-expansion; Diophantine approximation; Hausdorff dimension
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0025-5874