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Regular Interval Exchange Transformations over a Quadratic Field

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 نشر من قبل Francesco Dolce
 تاريخ النشر 2014
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف Francesco Dolce




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We describe a generalization of a result of Boshernitzan and Carroll: an extension of Lagranges Theorem on continued fraction expansion of quadratic irrationals to interval exchange transformations. In order to do this, we use a two-sided version of the Rauzy induction. In particular, we show that starting from an interval exchange transforma- tion whose lengths are defined over a quadratic field and applying the two-sided Rauzy induction, one can obtain only a finite number of new transformations up to homothety.



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