On metric properties of self-affine polygonal dendrites

Abstract

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