Slow entropy of higher rank abelian unipotent actions

2020/05/05 by Adam Kanigowski, Philipp Kunde, Kanigowski, Adam +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2005.02212

openalex publication_date 2020/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Lie(G) induced by 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.

Citations

• Survey on entropy-type invariants of sub-exponential growth in dynamical systems

Cited by

• Slow entropy of some combinatorial constructions
• Topological slow entropy, sequence entropy, and generalized [T,T^-1] systems

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