On mild mixing of special flows over irrational rotations under piecewise smooth functions
| dc.creator | Fraczek, Krzysztof | |
| dc.creator | Lemanczyk, Mariusz | |
| dc.date | 2006-01-18 | |
| dc.date | 2006-02-02 | |
| dc.date.accessioned | 2026-07-07T06:59:03Z | |
| dc.date.available | 2026-07-07T06:59:03Z | |
| dc.description | It is proved that all special flows over the rotation by an irrational $α$ with bounded partial quotients and under $f$ which is piecewise absolutely continuous with a non-zero sum of jumps are mildly mixing. Such flows are also shown to enjoy a condition which emulates the Ratner condition introduced in \cite{Rat}. As a consequence we construct a smooth vector--field on $\T^2$ with one singularity point such that the corresponding flow $(ϕ_t)_{t\in\R}$ preserves a smooth measure, its set of ergodic components consists of a family of periodic orbits and one component of positive measure on which $(ϕ_t)_{t\in\R}$ is mildly mixing and is spectrally disjoint from all mixing flows. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601430 | |
| dc.identifier | http://arxiv.org/abs/math/0601430 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107603 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A10, 37C40, 37E35 | |
| dc.title | On mild mixing of special flows over irrational rotations under piecewise smooth functions | |
| dc.type | text |