Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk

Yann Delaporte

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arXiv · 2507.13029

Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk

Yann Delaporte

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Abstract

We construct analytic pseudo-rotations on the sphere and the disk with specific properties. We obtain analytic pseudo-rotations which are ergodic. Then, in opposition to ergodicity, we construct analytic pseudo-rotations which exhibit a maximum order of local emergence. To achieve this, we apply a principle introduced by Berger, based on the Approximation by Conjugacy method of Anosov-Katok.

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Yann Delaporte. 2025-07-17. Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk. https://arxiv.org/abs/2507.13029

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