On one-point intersection property for self-similar fractals

Kirill Kamalutdinov; Andrei Tetenov

doi:10.1088/1361-6544/ab4e0e

On one-point intersection property for self-similar fractals

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Abstract

This was a long-standing question since 90s whether one-point intersection property for a self-similar set implies open set condition (OSC). We answer this question negatively. We give an example of a totally disconnected self-similar set K ⊂ ℝ which does not have OSC and has minimal overlap of its pieces, that is, all intersections of its pieces K_i∩K_j, i≠j are empty except only one, which is a single point.

Original language	English
Pages (from-to)	408-416
Number of pages	9
Journal	Nonlinearity
Volume	33
Issue number	1
DOIs	https://doi.org/10.1088/1361-6544/ab4e0e
Publication status	Published - 1 Jan 2020

Keywords

general position theorem
Hausdorff dimension
open set condition
self-similar set
weak separation property

OECD FOS+WOS

1.01.PN MATHEMATICS, APPLIED
1.01.UR PHYSICS, MATHEMATICAL

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10.1088/1361-6544/ab4e0e

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On one-point intersection property for self-similar fractals

Abstract

Keywords

OECD FOS+WOS

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