An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$

Valery V. Ryzhikov

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arXiv · 2405.19959

An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$

Valery V. Ryzhikov

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Abstract

For any natural $n$, and real $\alpha\geq 0$ we construct an ergodic automorphism $T$ such that its tensor powers $T^{\otimes n}$ have singular spectra if $n\leq 1+\alpha /2$, and Lebesgue if $n\, > 1+\alpha/2$.

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Valery V. Ryzhikov. 2024-05-30. An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$. https://arxiv.org/abs/2405.19959

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