Furstenberg counterexamples over Diophantine rotations
Abstract
We construct cocycles in T × 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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