Abstract
The induced transformation on a properly chosen interval of a 2-interval exchange transformation is a 2-interval exchange transformation again. This induction is explicitly integrated by using the simple continued fraction algorithm. Therefore, we can say that the simple continued fraction algorithm acts well as a ‘‘multiplicative Rauzy induction’’ on the family of 2-interval exchange transformations. Now, we have the following question; On what kind of family of 3-interval exchange transformations does the negative slope algorithm act well as a multiplicative Rauzy induction? The purpose of this paper is to give the answer to this question.
Citation
Kazuko Nakazawa. Koshiro Ishimura. Shunji Ito. "Negative slope algorithm and multiplicative Rauzy induction of 3-interval exchange transformations." Hiroshima Math. J. 39 (3) 451 - 468, November 2009. https://doi.org/10.32917/hmj/1257544217
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