论文标题
较高等级的慢熵Abelian Unipitent动作
Slow entropy of higher rank abelian unipotent actions
论文作者
论文摘要
我们在任何有限量均匀的均匀空间$ g/γ$上研究Abelian Unipotent Action $ U $的慢熵不变性。对于每个这样的动作，我们都表明，拓扑慢熵可以直接从$ \ operatatorName {lie}（g）$的特殊分解的维度计算，而$ \ operatatorName {lie}（lie}（u）$。此外，我们能够证明该动作的度量慢熵与其拓扑慢熵一致。作为推论，我们获得任何Abelian Horocyclic Action的复杂性仅与$ G $的尺寸有关。这将等级的结果概括为[A。 Kanigowski，K。Vinhage，D。Wei，Commun。数学。物理。 370（2019），没有。 2，449-474。
We study slow entropy invariants for abelian unipotent actions $U$ on any finite volume homogeneous space $G/Γ$. 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.
