Intersections of the pieces of self-similar dendrites in the plane

Klara Allabergenova, Mary Samuel and Andrei Tetenov

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

Abstract: We prove that each self-similar dendrite in the plane has the weak separation property and that the ramification orders of its points are bounded. We show that there are self-similar dendrites in the plane that satisfy the Open Set Condition, such that several pieces may intersect in the same non-trivial subdendrite.

Keywords: Self-similar set; Dendrite; Open set condition; Weak separation property; Intersection graph (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003576

DOI: 10.1016/j.chaos.2024.114805

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