On cocycles with values in the group SU(2)
| dc.creator | Fraczek, Krzysztof | |
| dc.date | 2000-02-15 | |
| dc.date.accessioned | 2026-07-07T04:33:53Z | |
| dc.date.available | 2026-07-07T04:33:53Z | |
| dc.description | In this paper we introduce the notion of degree for $C^1$-cocycles over irrational rotations on the circle with values in the group SU(2). It is shown that if a $C^1$-cocycle $ϕ:S^1\to SU(2)$ over an irrational rotation by $α$ has nonzero degree, then the skew product $S^1\times SU(2)\ni(x,g)\mapsto (x+α,gϕ(x))\in S^1\times SU(2)$ is not ergodic and the group of essential values of $ϕ$ is equal to the maximal Abelian subgroup of SU(2). Moreover, if $ϕ$ is of class $C^2$ (with some additional assumptions) the Lebesgue component in the spectrum of the skew product has countable multiplicity. Possible values of degree are discussed, too. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002120 | |
| dc.identifier | http://arxiv.org/abs/math/0002120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58694 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05 | |
| dc.title | On cocycles with values in the group SU(2) | |
| dc.type | text |