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Scaling dynamics of a cubic interval exchange transformation

J. H. Lowenstein·F. Vivaldi
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Abstract

We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes both dynamics and scaling, we characterize the periodic points of the scaling map in terms of generalised decimal expansions, where the base is the reciprocal of a Pisot number and the digits are algebraic integers. We establish rigorously some basic facts, and use extensive numerical experimentation to formulate a conjecture.

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J. H. Lowenstein, F. Vivaldi. 2007-03-19. Scaling dynamics of a cubic interval exchange transformation. https://arxiv.org/abs/math/0703556

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