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Homogeneous spectrum, Disjointness of Convolutions, and Mixing Properties of Dynamical Systems | | V. V. Ryzhikov
; | | Date: |
26 Jun 2012 | | Abstract: | In connection with Rokhlin’s question on an automorphism with a homogeneous
nonsimple spectrum, we indicate a class of measure-preserving maps $T$ such
that $T imes T$ has a homogeneous spectrum of multiplicity 2. The
automorphisms in question satisfy the condition $sigmaastsigmaperp sigma$,
where $sigma$ is the spectral measure of $T$. We also show that there is a
mixing automorphism possessing the above properties and their higher order
analogs. This work published in the pilot issue of Selected Russian
Mathematics, Vol.1 (1999), no.1, 13-24. It did not become available for
readers. Here we present the article one-to-one as a preprint. | | Source: | arXiv, 1206.6093 | | Services: | Forum | Review | PDF | Favorites | |
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