Furstenberg counterexamples over Diophantine rotations
Dynamical Systems
2024-12-11 v1
Abstract
We construct cocycles in 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.
Cite
@article{arxiv.2412.07484,
title = {Furstenberg counterexamples over Diophantine rotations},
author = {Nikolaos Karaliolios},
journal= {arXiv preprint arXiv:2412.07484},
year = {2024}
}