On the classification of fractal square dendrites

2023/06/19 by Drozdov, Dmitry, Tetenov, Andrei
#28A80 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2306.10842

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.

Related

• Self-Similar Dendrites Generated by Polygonal Systems in the Plane
• A Survey on the Topology of Fractal Squares
• On Bi-Lipschitz classification of fractal cubes possessing one-point intersection property
• Abstract Fractals
• On the classification of fractal squares