# American Institute of Mathematical Sciences

2018, 13: 1-42. doi: 10.3934/jmd.2018012

## Rational ergodicity of step function skew products

 1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel 2 School of Mathematics, Bristol University, Bristol BS8 1TW, UK

Dedicated to the memory of Roy Adler
JA: Partially supported by ISF grant No. 1599/13.
MB: Supported by ERC Grant Agreement n. 335989.
NC: Partially supported by ISF grant No. 1599/13 and ERC grant No. 678520.

Received  March 31, 2017 Revised  October 11, 2017 Published  December 2018

We study rational step function skew products over certain rotations of the circle proving ergodicity and bounded rational ergodicity when the rotation number is a quadratic irrational. The latter arises from a consideration of the asymptotic temporal statistics of an orbit as modelled by an associated affine random walk.

Citation: Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012
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