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arXiv · 2302.11088

Katok's special representation theorem for multidimensional Borel flows

Konstantin Slutsky
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Abstract

Katok's special representation theorem states that any free ergodic measure-preserving $\mathbb{R}^{d}$-flow can be realized as a special flow over a $\mathbb{Z}^{d}$-action. It provides a multidimensional generalization of the "flow under a function" construction. We prove the analog of Katok's theorem in the framework of Borel dynamics and show that, likewise, all free Borel $\mathbb{R}^{d}$-flows emerge from $\mathbb{Z}^{d}$-actions through the special flow construction using bi-Lipschitz cocycles.

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Konstantin Slutsky. 2023-02-22. Katok's special representation theorem for multidimensional Borel flows. https://arxiv.org/abs/2302.11088

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