Slow Entropy of Some Parabolic Flows
Slow Entropy of Some Parabolic Flows
复制标题
一些抛物线流的慢熵
DOI：
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发表时间：
2017
影响因子：
2.4
通讯作者：
Daren Wei
中科院分区：
文献类型：
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作者：
Adam Kanigowski;Kurt Vinhage;Daren Wei
研究了齐次空间上一类抛物型流的非平凡熵不变量。我们证明拓扑复杂性（即慢熵）可以直接从伴随表示的乔丹块结构计算。此外，使用一致多项式剪切，我们能够证明度量轨道增长（即慢熵）与拓扑轨道增长一致，从而建立了准单幂流的变分原理（这也适用于非紧化情况）。我们的结果也适用于序列熵。我们建立了一个系统具有平凡拓扑复杂性的判据，并给出了一些唯一遍历系统的测量理论复杂性和拓扑复杂性不重合的例子，违反了经典变分原理的直觉。
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the adjoint representation. Moreover using uniform polynomial shearing we are able to show that the metric orbit growth (ie, slow entropy) coincides with the topological one, establishing hence variational principle for quasi-unipotent flows (this also applies to the non-compact case). Our results also apply to sequence entropy. We establish criterion for a system to have trivial topological complexity and give some examples in which the measure-theoretic and topological complexities do not coincide for uniquely ergodic systems, violating the intuition of the classical variational principle.