Generic smooth cocycles of degree zero over irrational rotations
Iwanik, A.
Studia Mathematica, Tome 113 (1995), p. 241-250 / Harvested from The Polish Digital Mathematics Library
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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 C1 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 Cr cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic C1 cocycles the speed can be improved to o(1/(nlogn)). For generic α and generic Cr cocycles (r = 1,...,∞) the spectral measure of the skew product has a continuous component and Hausdorff dimension zero.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216210 
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Iwanik, A. Generic smooth cocycles of degree zero over irrational rotations. Studia Mathematica, Tome 113 (1995) pp. 241-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv115i3p241bwm/

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