Displaying similar documents to “Cyclic approximation of ergodic step cocycles over irrational rotations”

Generic smooth cocycles of degree zero over irrational rotations

A. Iwanik (1995)

Studia Mathematica

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If a rotation α of has unbounded partial quotients then “most” of its skew-product diffeomorphic extensions to the 2-torus × defined by C 1 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 C r cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic C 1 cocycles the speed can be improved to o(1/(nlogn))....