On metric properties of self-affine polygonal dendrites
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 $diam(γ)\le C |x-y|^λ$.
math.MG↗