Minimal Dynamical Systems and Approximate Conjugacy
| dc.creator | Lin, Huaxin | |
| dc.creator | Matui, Hiroki | |
| dc.date | 2004-02-19 | |
| dc.date.accessioned | 2026-07-07T05:05:35Z | |
| dc.date.available | 2026-07-07T05:05:35Z | |
| dc.description | Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product $C^*$-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via $K$-theory and $C^*$-algebras. For example, it is shown that two Cantor minimal systems are approximately $τ$-conjugate if and only if they are orbit equivalent and have the same periodic spectrum. It is also shown that two such systems are approximately $K$-conjugate if and only if the corresponding crossed product $C^*$-algebras have the same scaled ordered $K$-theory. Consequently, two Cantor minimal systems are approximately $K$-conjugate if and only if the associated transformation $C^*$-algebras are isomorphic. Incidentally, this approximate $K$-conjugacy coincides with Giordano, Putnam and Skau's strong orbit equivalence for the Cantor minimal systems. | |
| dc.identifier | https://arxiv.org/abs/math/0402309 | |
| dc.identifier | http://arxiv.org/abs/math/0402309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70216 | |
| dc.subject | Operator Algebras | |
| dc.title | Minimal Dynamical Systems and Approximate Conjugacy | |
| dc.type | text |