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Journal of Dynamical and Control Systems

, Volume 19, Issue 4, pp 569–573 | Cite as

The Hausdorff Dimension of the Support of the Erdös Measure and Symbolic Dynamics

  • Z. I. Bezhaeva
  • V. I. Oseledets
Article
  • 113 Downloads

Abstract

Algorithm is given for computation of the Hausdorff dimension of the support of the Erdos measure for a Pisot number.

Keywords

Hausdorff dimension Pisot number Erdos measure Sofic set Deterministic automaton Entropy 

Mathematics Subject Classifications (2010)

28D05 28D20 37B10 11K55 

Notes

Acknowledgements

The work was supported by RFBR grant 11-01-00982. The study was carried out within “The National High School of Economics” Academic fund program in 2013–2014 (grant no. 12-01-005C)

References

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    Bezhaeva ZI, Oseledets VI. Erdös measures, sofic measures, and Markov chains. Zap Nauch Sem POMI. 2005;326:28–47 (in Russian).MATHGoogle Scholar
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    Bezhaeva ZI, Oseledets VI. Erdös measures, sofic measures, and Markov chains. J Math Sci. 2007;120:28–47.MathSciNetGoogle Scholar
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    Pollicott M, Simon K. Hausdorff dimension λ-expansions with deleted digits. Trans Am Math Soc. 1995;347:967–83.MathSciNetMATHGoogle Scholar
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    Kean M, Smorodinsky M, Solomyak B. On the morphology of γ-expansions with deleted digits. Trans Am Math Soc. 1995;347:955–66.Google Scholar
  5. 5.
    Lalley Steven P. β-expansions with deleted digits for Pisot numbers β. Trans Am Math Soc. 1997;347:4355–65.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.MIEM NRU HSEMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia
  3. 3.Financial UniversityMoscowRussia

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