On the classification of fractal square dendrites Full article
| Journal |
Advances in the Theory of Nonlinear Analysis and its Applications
, E-ISSN: 2587-2648 |
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| Output data | Year: 2023, Volume: 7, Number: 3, Article number : 276, Pages count : 18 DOI: 10.17762/atnaa.v7.i3.276 | ||||
| Tags | fractal square, dendrite, self-similar boundary, main tree, ramification point | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
We consider the classification of fractal square dendrites K based on the types of the self-similar boundary ∂K and the main tree γ of such dendrites. We show that the self-similar boundary of a fractal square dendrite K may be of 5 possible types and may consist of 3,4 or 6 points. We prove that the main trees of fractal square dendrites belong to 7 possible classes. Bearing in mind the placement and orders of the points of ∂K with respect to the main tree γ, this results in 16 possible types of main trees for non-degenerate fractal square dendrites.
Cite:
Drozdov D.A.
, Tetenov A.V.
On the classification of fractal square dendrites
Advances in the Theory of Nonlinear Analysis and its Applications. 2023. V.7. N3. 276 :1-18. DOI: 10.17762/atnaa.v7.i3.276 Scopus РИНЦ OpenAlex
On the classification of fractal square dendrites
Advances in the Theory of Nonlinear Analysis and its Applications. 2023. V.7. N3. 276 :1-18. DOI: 10.17762/atnaa.v7.i3.276 Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Aug 4, 2023 |
| Accepted: | Oct 12, 2023 |
| Published print: | Oct 25, 2023 |
| Published online: | Oct 25, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85189522604 |
| Elibrary: | 65561285 |
| OpenAlex: | W4393342697 |