On an abrasion motivated fractal model

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Bibliographic Details
Main Authors:	Bárány, Balázs, Domokos, Gábor, Szesztay, Ágoston
Format:	Preprint
Published:	2024
Subjects:	Dynamical Systems
Online Access:	Acceder al recurso
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author	Bárány, Balázs Domokos, Gábor Szesztay, Ágoston
author_facet	Bárány, Balázs Domokos, Gábor Szesztay, Ágoston
contents	In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_17765
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	On an abrasion motivated fractal model Bárány, Balázs Domokos, Gábor Szesztay, Ágoston Dynamical Systems In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.
title	On an abrasion motivated fractal model
topic	Dynamical Systems
url	https://arxiv.org/abs/2402.17765

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