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arXiv · 2208.12174

An example of a weakly mixing BV vector field which is not strongly mixing

Martina Zizza
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Abstract

We give an example of a weakly mixing vector field $b\in L^\infty([0,1],\text{BV}(\mathbb{T}^2))$ which is not strongly mixing. The example is based on a work of Chacon who constructed a weakly mixing automorphism which is not strongly mixing on $([0,1],\mathcal{B}([0,1]),|\cdot|)$, where $\mathcal{B}([0,1])$ are the Borel subsets of $[0,1]$ and $|\cdot|$ is the one-dimensional Lebesgue measure.

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Martina Zizza. 2022-08-25. An example of a weakly mixing BV vector field which is not strongly mixing. https://arxiv.org/abs/2208.12174

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