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Rational ergodicity of step function skew products

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.

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  • 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.

    Mathematics Subject Classification: Primary: 37A40; Secondary: 11K38, 60F05.


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