Ergodic-theoretic properties of certain Bernoulli convolutions
| dc.creator | Sidorov, Nikita | |
| dc.date | 2002-03-06 | |
| dc.date.accessioned | 2026-07-07T04:46:52Z | |
| dc.date.available | 2026-07-07T04:46:52Z | |
| dc.description | In [17] the author and A. Vershik have shown that for $\be=\frac12(1+\sqrt5)$ and the alphabet $\{0,1\}$ the infinite Bernoulli convolution ($=$ the Erdös measure) has a property similar to the Lebesgue measure. Namely, it is quasi-invariant of type $\mathrm{II}_1$ under the $\be$-shift, and the natural extension of the $\be$-shift provided with the measure equivalent to the Erdös measure, is Bernoulli. In this note we extend this result to all Pisot parameters $\be$ (modulo some general arithmetic conjecture) and an arbitrary "sufficient" alphabet. | |
| dc.description | 10 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0203056 | |
| dc.identifier | http://arxiv.org/abs/math/0203056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63504 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Number Theory | |
| dc.subject | 28D05; 11R06 | |
| dc.title | Ergodic-theoretic properties of certain Bernoulli convolutions | |
| dc.type | text |