Generic smooth cocycles of degree zero over irrational rotations
Studia Mathematica, Tome 115 (1995) no. 3, p. 241.

Voir la notice de l'article dans European Digital Mathematics Library

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)). For generic α and generic C r cocycles (r = 1,...,∞) the spectral measure of the skew product has a continuous component and Hausdorff dimension zero.
Classification : 28D05
Mots-clés : Anzai skew product, weakly mixing cocycle, cyclic approximation, simple spectrum, cocycles, skew product diffeomorphisms 
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     title = {Generic smooth cocycles of degree zero over irrational rotations},
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A. Iwanik. Generic smooth cocycles of degree zero over irrational rotations. Studia Mathematica, Tome 115 (1995) no. 3, p. 241. https://geodesic-test.mathdoc.fr/item/STUMA_1995__115_3_216210/