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arXiv · 1812.00392

Maximally highly proximal flows

Andy Zucker
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Abstract

For $G$ a Polish group, we consider $G$-flows which either contain a comeager orbit or have all orbits meager. We single out a class of flows, the maximally highly proximal (MHP) flows, for which this analysis is particularly nice. In the former case, we provide a complete structure theorem for flows containing comeager orbits, generalizing theorems of Melleray-Nguyen Van Th\'e-Tsankov and Ben Yaacov-Melleray-Tsankov. In the latter, we show that any minimal MHP flow with all orbits meager has a metrizable factor with all orbits meager, thus "reflecting" complicated dynamical behavior to metrizable flows. We then apply this to obtain a structure theorem for Polish groups whose universal minimal flow is distal.

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Andy Zucker. 2018-12-02. Maximally highly proximal flows. https://doi.org/10.1017/etds.2020.40

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