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arXiv · 2605.03990

On metric properties of self-affine polygonal dendrites

Andrei Tetenov·Ivan Yudin·Dilmurat Kutlimuratov
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Abstract

We prove that for any self-affine dendrite K generated by a polygonal system, there are constants C>0 and $λ\in(0, 1)$ such that for any x, y in K, the Jordan arc $γ$ in K with endpoints x, y satisfies the inequality $diam(γ)\le C |x-y|^λ$.

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Andrei Tetenov, Ivan Yudin, Dilmurat Kutlimuratov. 2026-05-05. On metric properties of self-affine polygonal dendrites. https://arxiv.org/abs/2605.03990

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