Generic smooth cocycles of degree zero over irrational rotations
A. Iwanik (1995)
Studia Mathematica
Similarity:
If a rotation α of has unbounded partial quotients then “most” of its skew-product diffeomorphic extensions to the 2-torus × defined by cocycles of topological degree zero enjoy nontrivial ergodic properties. In fact they admit a cyclic approximation with speed o(1/n) and have nondiscrete (simple) spectrum. Similar results are obtained for cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic cocycles the speed can be improved to o(1/(nlogn))....