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arXiv · 2412.07484

Furstenberg counterexamples over Diophantine rotations

Nikolaos Karaliolios
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Abstract

We construct cocycles in $\mathbb{T} \times SU(2)$ over Diophantine rotations that are minimal and not uniquely ergodic. Such cocycles are dense in an open subset of cocycles over the fixed Diophantine rotation. By a standard argument, they are dense in the whole set of such cocycles if the rotation satisfies a full-measure arithmetic condition.

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Nikolaos Karaliolios. 2024-12-10. Furstenberg counterexamples over Diophantine rotations. https://arxiv.org/abs/2412.07484

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