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 -