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arXiv · 1206.6093

Homogeneous spectrum, Disjointness of Convolutions, and Mixing Properties of Dynamical Systems

V. V. Ryzhikov
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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 $T\times T$ has a homogeneous spectrum of multiplicity 2. The automorphisms in question satisfy the condition $σ\astσ\perp σ$, where $σ$ 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 has been published in the pilot issue of Selected Russian Mathematics, Vol.1 (1999), no.1, 13-24.

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V. V. Ryzhikov. 2012-06-27. Homogeneous spectrum, Disjointness of Convolutions, and Mixing Properties of Dynamical Systems. https://arxiv.org/abs/1206.6093

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