Ergodicity of cocycles over 2-dimensional rotations
Volume 287 / 2026
Studia Mathematica 287 (2026), 105-143
MSC: Primary 28D05; Secondary 22D40, 37A25, 37A45, 11K60
DOI: 10.4064/sm250131-29-10
Published online: 6 March 2026
Abstract
We study recurrence and ergodicity of cocycles with values in $\mathbb {R}^d$, $d \geq 1$, over a rotation on $\mathbb {T}^\rho $, $\rho \gt 1$, under Diophantine conditions for the rotation and the discontinuities of the functions generating the cocycles. For simplicity of notation we mainly consider the cases $\rho = 2$, $d=1$ and 2.
