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Completely uniformly distributed sequences of matrices

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Number-Theoretic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1452))

Abstract

It is proved that for almost all s × s-matrices A with largest eigenvalue λ(A)>1 the sequence of powers (A p(n)) ∞n=1 is completely uniformly distributed modulo 1, where p(n) are different positive integers. Furthermore a constructive example for a matrix A is given such that the sequence (A n) ∞n=1 is completely uniformly distributed.

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References

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Author information

Authors and Affiliations

  1. Department of Discrete Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    M. Drmota

  2. Department of Technical Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    R. F. Tichy

  3. Department of Algebra, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    R. Winkler

Authors
  1. M. Drmota
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  2. R. F. Tichy
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  3. R. Winkler
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Editor information

Edmund Hlawka Robert F. Tichy

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© 1990 Springer-Verlag

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Drmota, M., Tichy, R.F., Winkler, R. (1990). Completely uniformly distributed sequences of matrices. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096980

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  • DOI: https://doi.org/10.1007/BFb0096980

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53408-2

  • Online ISBN: 978-3-540-46864-6

  • eBook Packages: Springer Book Archive

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