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On the classification of fractal square dendrites. / Drozdov, Dmitry; Tetenov, Andrei.

In: Advances in the Theory of Nonlinear Analysis and its Applications, Vol. 7, No. 3, 07.11.2023, p. 79-96.

Research output: Contribution to journal › Article › peer-review

Harvard

Drozdov, D & Tetenov, A 2023, 'On the classification of fractal square dendrites', Advances in the Theory of Nonlinear Analysis and its Applications, vol. 7, no. 3, pp. 79-96. https://doi.org/10.17762/atnaa.v7.i3.276

APA

Drozdov, D., & Tetenov, A. (2023). On the classification of fractal square dendrites. Advances in the Theory of Nonlinear Analysis and its Applications, 7(3), 79-96. https://doi.org/10.17762/atnaa.v7.i3.276

Vancouver

Drozdov D, Tetenov A. On the classification of fractal square dendrites. Advances in the Theory of Nonlinear Analysis and its Applications. 2023 Nov 7;7(3):79-96. doi: 10.17762/atnaa.v7.i3.276

Author

Drozdov, Dmitry ; Tetenov, Andrei. / On the classification of fractal square dendrites. In: Advances in the Theory of Nonlinear Analysis and its Applications. 2023 ; Vol. 7, No. 3. pp. 79-96.

BibTeX

@article{693cf2de774a4f4994cc3c81f7b28783,
title = "On the classification of fractal square dendrites",
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.",
keywords = "dendrite, fractal square, main tree, ramification point, self-similar boundary",
author = "Dmitry Drozdov and Andrei Tetenov",
note = "The work is supported by the Mathematical Center in Akademgorodok under the agreement no.075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.",
year = "2023",
month = nov,
day = "7",
doi = "10.17762/atnaa.v7.i3.276",
language = "English",
volume = "7",
pages = "79--96",
journal = "Advances in the Theory of Nonlinear Analysis and its Applications",
issn = "2587-2648",
publisher = "Erdal KARAPINAR",
number = "3",

}

RIS

TY - JOUR

T1 - On the classification of fractal square dendrites

AU - Drozdov, Dmitry

AU - Tetenov, Andrei

N1 - The work is supported by the Mathematical Center in Akademgorodok under the agreement no.075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2023/11/7

Y1 - 2023/11/7

N2 - 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.

AB - 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.

KW - dendrite

KW - fractal square

KW - main tree

KW - ramification point

KW - self-similar boundary

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85189522604&origin=inward&txGid=7b1ffae169de618a2cac5e94305e6305

UR - https://www.mendeley.com/catalogue/1313e89f-b670-39ce-b6cc-3775ee3ca256/

U2 - 10.17762/atnaa.v7.i3.276

DO - 10.17762/atnaa.v7.i3.276

M3 - Article

VL - 7

SP - 79

EP - 96

JO - Advances in the Theory of Nonlinear Analysis and its Applications

JF - Advances in the Theory of Nonlinear Analysis and its Applications

SN - 2587-2648

IS - 3

ER -

ID: 59888312