# American Institute of Mathematical Sciences

September  2020, 40(9): 5105-5116. doi: 10.3934/dcds.2020220

## Renormalizing an infinite rational IET

 1 The City College of New York New York, NY, 10031, USA 2 CUNY Graduate Center New York, NY, 10016, USA 3 University of Toronto Toronto, ON, M5S 2E4, Canada

Received  September 2018 Revised  October 2019 Published  June 2020

We study an interval exchange transformation of $[0, 1]$ formed by cutting the interval at the points $\frac{1}{n}$ and reversing the order of the intervals. We find that the transformation is periodic away from a Cantor set of Hausdorff dimension zero. On the Cantor set, the dynamics are nearly conjugate to the $2$–adic odometer.

Citation: W. Patrick Hooper, Kasra Rafi, Anja Randecker. Renormalizing an infinite rational IET. Discrete & Continuous Dynamical Systems, 2020, 40 (9) : 5105-5116. doi: 10.3934/dcds.2020220
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##### References:
Top: The interval $[0,1)$ cut into intervals of the form $[1-\frac{1}{k},1-\frac{1}{k+1})$. Bottom: The images of these intervals under $T_1$
The intervals $I_{w0}$ and $I_{w1}$ produced from $I_w$ when $s_{|w|} = \frac{1}{4}$
The construction of the Cantor set ${{\mathcal{C}}}$ when $N = 1$
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