- Tytuł:
- Generic smooth cocycles of degree zero over irrational rotations
- Autorzy:
- Iwanik, Anzelm
- Powiązania:
- https://bibliotekanauki.pl/articles/1288978.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Anzai skew product
weakly mixing cocycle
cyclic approximation
simple spectrum - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1995, 115, 3; 241-250
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł