A two dimensional analog of the three gap theorem

2023/08/03 by Yury Kochetkov, Kochetkov, Yury, Alexandr Osipov +1
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2308.01848

Abstract

For a two dimensional vector v=(α,β), where α>0, β>0 are irrational numbers independent over ℚ, we consider the set D_n=\(iα \rm mod 1,iβ \rm mod 1),i=1,…,n\ in a two dimensional torus and the partition of this torus into Voronoi cells. Areas and forms of these cells are the subject of this experimental work.

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