Parametric Geometry of Numbers with General Flow

2021/06/03 by Omri N. Solan, Omri Nisan Solan, Solan, Omri Nisan · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS

paper · pdf · doi:10.48550/arxiv.2106.01707

openalex publication_date 2021/06/03 · arxiv created 2021/07/24 · arxiv updated 2021/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend results of parametric geometry of numbers to a general diagonal flow on the space of lattices. Moreover, we compute the Hausdorff dimension of the set of trajectories with every given behavior, with respect to a nonstandard metric and thereby attain bounds on the standard ones.

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• Slowly Divergent Trajectories for Weighted Singular Vectors in R²

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