A dynamical system using the Voronoi tessellation

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We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the behavior of this system for small point sets, then prove a general result quantifying the growth of the sizes of the point sets under iteration. We conclude by giving the most interesting open problems.
13 pages, 8 figures

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Dynamical Systems, Mathematical Physics, 37E99;52C20

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http://salesiana.dossiersoluciones.com/handle/123456789/144763

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.3736
 http://arxiv.org/abs/0712.3736

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arXiv