Scaling dynamics of a cubic interval exchange transformation
Dynamical Systems
2007-05-23 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.math/0703556,
title = {Scaling dynamics of a cubic interval exchange transformation},
author = {J. H. Lowenstein and F. Vivaldi},
journal= {arXiv preprint arXiv:math/0703556},
year = {2007}
}
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18 pages