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arXiv · 2005.02212

Slow entropy of higher rank abelian unipotent actions

Adam Kanigowski·Philipp Kunde·Kurt Vinhage·Daren Wei
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Abstract

We study slow entropy invariants for abelian unipotent actions $U$ on any finite volume homogeneous space $G/\Gamma$. For every such action we show that the topological slow entropy can be computed directly from the dimension of a special decomposition of $\operatorname{Lie}(G)$ induced by $\operatorname{Lie}(U)$. Moreover, we are able to show that the metric slow entropy of the action coincides with its topological slow entropy. As a corollary, we obtain that the complexity of any abelian horocyclic action is only related to the dimension of $G$. This generalizes the rank one results from [A. Kanigowski, K. Vinhage, D. Wei, Commun. Math. Phys. 370 (2019), no. 2, 449-474.] to higher rank abelian actions.

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Adam Kanigowski, Philipp Kunde, Kurt Vinhage, Daren Wei. 2020-05-05. Slow entropy of higher rank abelian unipotent actions. https://arxiv.org/abs/2005.02212

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