On the intersection of fractal cubes

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Bibliographic Details
Main Authors:	Tetenov, Andrei, Drozdov, Dmitry
Format:	Preprint
Published:	2024
Subjects:	Metric Geometry 28A80
Online Access:	Acceder al recurso
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_version_	1866910633214083072
author	Tetenov, Andrei Drozdov, Dmitry
author_facet	Tetenov, Andrei Drozdov, Dmitry
contents	We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of such intersection as the attractor of a graph-directed system of similarities in terms of the sets of units corresponding to these cubes and intersections of pairs of l-faces. As a corollary, we prove dimension formula for the intersection and the condition of finiteness of its measure. Another corollary gives the conditions under which the intersections have the given cardinality. Applying these techniques, we obtain the conditions under which a fractal k-cube has the finite intersection property and the conditions under which the fractal cube is a dendrite.
format	Preprint
id	arxiv_https___arxiv_org_abs_2410_03388
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	On the intersection of fractal cubes Tetenov, Andrei Drozdov, Dmitry Metric Geometry 28A80 We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of such intersection as the attractor of a graph-directed system of similarities in terms of the sets of units corresponding to these cubes and intersections of pairs of l-faces. As a corollary, we prove dimension formula for the intersection and the condition of finiteness of its measure. Another corollary gives the conditions under which the intersections have the given cardinality. Applying these techniques, we obtain the conditions under which a fractal k-cube has the finite intersection property and the conditions under which the fractal cube is a dendrite.
title	On the intersection of fractal cubes
topic	Metric Geometry 28A80
url	https://arxiv.org/abs/2410.03388

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