Superdensity and super-micro-uniformity in non-integrable flat systems

2021/09/10 by József Beck, Beck, J., W.W.L. Chen +1
Computer Science · Mathematics · #11K38 #37E35 #Computational Geometry and Mesh Generation #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2109.04836

openalex publication_date 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that on any non-integrable finite polysquare translation surface, superdensity, an optimal form of time-quantitative density, leads to an optimal form of time-quantitative uniformity that we call super-micro-uniformity.

Related

• Time-quantitative density of non-integrable systems
• Quantitative behavior of non-integrable systems (III)
• Quantitative behavior of non-integrable systems (IV)
• Super-fast spreading of billiard orbits in rational polygons and geodesics on translation surfaces
• Uniformity in cube-covering systems