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

Author

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  • Allabergenova, Klara
  • Samuel, Mary
  • Tetenov, Andrei

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.

Suggested Citation

  • Allabergenova, Klara & Samuel, Mary & Tetenov, Andrei, 2024. "Intersections of the pieces of self-similar dendrites in the plane," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003576
    DOI: 10.1016/j.chaos.2024.114805
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