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Symmetric interval identification systems of order three

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  • In the present paper we study symmetric interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order 3 after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of symmetric interval identification system of thin type.
    Mathematics Subject Classification: Primary: 37E05, 37E25; Secondary: 57M99.

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