Skip to main content
Log in

Universal β-expansions

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. J.-P. Allouche and J. Shallit, The ubiquitous Prouhet–Thue–Morse sequence, ed. by C. Ding. T. Helleseth, and H. Niederreiter, Sequences and Their Applications: Proceedings of SETA '98, Springer-Verlag, 1999, 1–16.

  2. A. Bertrand-Mathis, Points génériques de Champernowne sur certains systèmes codés; application aux θ-shifts, Ergodic Theory Dynam.Systems 8 (1988), 35–51.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. ErdŐs, On a family of symmetric Bernoulli convolutions, Amer.J.Math. 61 (1939), 974–975.

    Article  MathSciNet  Google Scholar 

  4. P. ErdŐs, I. Joó and V. Komornik, Characterization of the unique expansions \(1 = \sum\nolimits_{i = 1}^\infty {q^{ - n_i } }\) and related problems, Bull.Soc.Math.Fr. 118 (1990), 377–390.

    Google Scholar 

  5. P. Erdós and V. Komornik, Developments in non-integer bases, Acta Math.Hungar. 79 (1998), 57–83.

    Article  MathSciNet  Google Scholar 

  6. S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math. 206 (1999), 145–154.

    Article  MATH  MathSciNet  Google Scholar 

  7. Ch. Frougny, Representations of numbers and finite automata, Math.Systems Theory 25 (1992), 37–60.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Glendinning and N. Sidorov, Unique representations of real numbers in non-integer bases, Math.Res.Lett. 8 (2001), 535–543.

    MATH  MathSciNet  Google Scholar 

  9. V. Komornik and P. Loretti, Unique developments in non-integer bases, Amer.Math.Monthly 105 (1998), 636–639.

    Article  MATH  MathSciNet  Google Scholar 

  10. W. Parry, On the ß-expansions of real numbers, Acta Math.Acad.Sci.Hung. 11 (1960), 401–416.

    Article  MATH  MathSciNet  Google Scholar 

  11. Y. Peres, W. Schlag and B. Solomyak, Sixty years of Bernoulli convolutions, Fractal geometry and stochastics, II (Greifswald/Koserow, 1998), 39–65, Progr. Probab., 46, Birkhauser, Basel, 2000.

    Google Scholar 

  12. A. Rényi, Representations for real numbers and their ergodic properties, Acta Math.Acad.Sci.Hung. 8 (1957) 477–493.

    Article  MATH  Google Scholar 

  13. N. Sidorov, Almost every number has a continuum of ß-expansions, Amer.Math.Monthly 110 (2003), 838–842.

    MATH  MathSciNet  Google Scholar 

  14. N. Sidorov, Arithmetic dynamics, London Math.Soc.Lecture Notes Ser. 310 (2003), 145–189.

    MATH  MathSciNet  Google Scholar 

  15. N. Sidorov, Ergodic-theoretic properties of certain Bernoulli convolutions, Acta Math.Hungar. 101 (2003), 345–355.

    Article  MATH  MathSciNet  Google Scholar 

  16. N. Sidorov and A. Vershik, Ergodic properties of Erdós measure, the entropy of the goldenshift, and related problems, Monatsh.Math. 126 (1998), 215–261.

    Article  MATH  MathSciNet  Google Scholar 

  17. B. Solomyak, On the random series \(\sum { \pm \lambda ^i }\) (an Erdós problem), Ann.Math. (2) 142 (1995), 611–625.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sidorov, N. Universal β-expansions. Periodica Mathematica Hungarica 47, 221–231 (2003). https://doi.org/10.1023/B:MAHU.0000010823.98226.4e

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:MAHU.0000010823.98226.4e

Navigation