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

På svenska

Author

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 .

Department/s

Publishing year

2014

Language

English

Pages

799-827

Publication/Series

Mathematische Zeitschrift

Volume

276

Issue

3-4

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • beta-expansion
  • Diophantine approximation
  • Hausdorff dimension

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0025-5874