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arXiv · 2306.10842

On the classification of fractal square dendrites

Dmitry Drozdov·Andrei Tetenov
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Abstract

We consider the classification of fractal square dendrites $K$ based on the types of the self-similar boundary $\partial K$ and the main tree $\gamma$ 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 $\partial K$ with respect to the main tree $\gamma$, this results in 16 possible types of main trees for non-degenerate fractal square dendrites.

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Dmitry Drozdov, Andrei Tetenov. 2023-06-19. On the classification of fractal square dendrites. https://arxiv.org/abs/2306.10842

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