Ergodic-theoretic properties of certain Bernoulli convolutions

dc.creatorSidorov, Nikita
dc.date2002-03-06
dc.date.accessioned2026-07-07T04:46:52Z
dc.date.available2026-07-07T04:46:52Z
dc.descriptionIn [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.description10 pages, Latex2e
dc.identifierhttps://arxiv.org/abs/math/0203056
dc.identifierhttp://arxiv.org/abs/math/0203056
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63504
dc.subjectDynamical Systems
dc.subjectNumber Theory
dc.subject28D05; 11R06
dc.titleErgodic-theoretic properties of certain Bernoulli convolutions
dc.typetext

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