Furstenberg Transformations and Approximate Conjugacy
| dc.creator | Lin, Huaxin | |
| dc.date | 2005-05-02 | |
| dc.date.accessioned | 2026-07-07T05:19:35Z | |
| dc.date.available | 2026-07-07T05:19:35Z | |
| dc.description | Let $α$ and $β$ be two Furstenberg transformations on 2-torus associated with irrational numbers $θ_1,$ $θ_2,$ integers $d_1, d_2$ and Lipschitz functions $f_1$ and $f_2.$ We show that $α$ and $β$ are approximately conjugate in a measure theoretical sense if (and only if) $\bar{θ_1\pm θ_2}=0$ in $\R/\Z.$ Closely related to the classification of simple amenable $C^*$-algebras, we show that $α$ and $β$ are approximately $K$-conjugate if (and only if) $\bar{θ_1\pm θ_2}=0$ in $\R/\Z$ and $|d_1|=|d_2|.$ This is also shown to be equivalent to that the associated crossed product $C^*$-algebras are isomorphic. | |
| dc.identifier | https://arxiv.org/abs/math/0505028 | |
| dc.identifier | http://arxiv.org/abs/math/0505028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75066 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 4635 | |
| dc.title | Furstenberg Transformations and Approximate Conjugacy | |
| dc.type | text |