Drozdov, D., & Tetenov, A. (2023). On the classification of fractal square dendrites. Advances in the Theory of Nonlinear Analysis and Its Application, 7(3), 79–96.
- ISSN: 2587-2648
Menu
Dmitry Drozdova,b, Andrei Tetenova
a Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia.
b Novosibirsk State University, Novosibirsk, 630090, Russia.
We consider the classification of fractal square dendrites 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 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: Fractal square, dendrite, self-similar boundary, main tree, ramification point.
Drozdov, D., & Tetenov, A. (2023). On the classification of fractal square dendrites. Advances in the Theory of Nonlinear Analysis and Its Application, 7(3), 79–96.