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Absorbing sets of homogeneous subtractive algorithms

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Abstract

We consider homogeneous multidimensional continued fraction algorithms, in particular a family of maps which was introduced by F. Schweiger. We prove his conjecture regarding the existence of an absorbing set for those maps. We also establish that their renormalisations are nonergodic which disproves another conjecture due to Schweiger. Other homogeneous algorithms are also analysed including ones which are ergodic.

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy, 163, avenue de Luminy, Case 907, 13288, Marseille Cedex 9, France

    Tomasz Miernowski & Arnaldo Nogueira

Authors
  1. Tomasz Miernowski
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  2. Arnaldo Nogueira
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Correspondence to Arnaldo Nogueira.

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Communicated by K. Schmidt.

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Miernowski, T., Nogueira, A. Absorbing sets of homogeneous subtractive algorithms. Monatsh Math 167, 547–569 (2012). https://doi.org/10.1007/s00605-012-0385-x

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  • DOI: https://doi.org/10.1007/s00605-012-0385-x

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