On one-point intersection property for self-similar fractals Full article
| Journal |
Nonlinearity
ISSN: 0951-7715 , E-ISSN: 1361-6544 |
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| Output data | Year: 2020, Volume: 33, Number: 1, Pages: 408 Pages count : 9 DOI: 10.1088/1361-6544/ab4e0e | ||||
| Tags | self-similar set, open set condition, weal separation property, Hausdorff dimension, single intersection property | ||||
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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 which does not have OSC and has minimal overlap of its pieces, that is, all intersections of its pieces are empty except only one, which is a single point.
Cite:
Tetenov A.
, Kamalutdinov K.
On one-point intersection property for self-similar fractals
Nonlinearity. 2020. V.33. N1. P.408. DOI: 10.1088/1361-6544/ab4e0e WOS Scopus OpenAlex
On one-point intersection property for self-similar fractals
Nonlinearity. 2020. V.33. N1. P.408. DOI: 10.1088/1361-6544/ab4e0e WOS Scopus OpenAlex
Dates:
| Submitted: | Jan 17, 2019 |
| Accepted: | Oct 15, 2019 |
| Published print: | Dec 4, 2019 |
| Published online: | Dec 4, 2019 |
Identifiers:
| Web of science: | WOS:000632837000001 |
| Scopus: | 2-s2.0-85081312195 |
| OpenAlex: | W2992232891 |